Alternative to "easy to see" in maths texts.

[Paul]

Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
Here's a typical example:
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."

However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that
the reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying to reassure
the reader that to "see" the truth of the claim, the text is sufficient,
and other theorems and texts are not required.

But none of this is easy, and I wonder whether students might not realise
that "easy" is being used in a slightly atypical way, and worry unneccessarily
if seeing something "easy" takes them several hours.

Maybe "straightforward to see" would be more accurate perhaps, because the
process of understanding the text is straightforward (but not easy).

Any opinions?

Paul

[s***@gmail.com]

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that
the reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying to reassure
the reader that to "see" the truth of the claim, the text is sufficient,
and other theorems and texts are not required.
But none of this is easy, and I wonder whether students might not realise
that "easy" is being used in a slightly atypical way, and worry unneccessarily
if seeing something "easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps, because the
process of understanding the text is straightforward (but not easy).
Any opinions?

In my experience, "easy to see" in a math or physics context means that
it only takes a typical professor 5 minutes
to sketch the proof/derivation/etcon the chalkboard
(whiteboards came in after I passed the last undergraduate milestone).

Usually it also means "we're saving trees by not filling in those details
within this already voluminous text".

/dps

[Stefan Ram]

Post by s***@gmail.com
In my experience, "easy to see" in a math or physics context means that

An alternative to "easy to see" is "left as an exercise".

[Dr. Jai Maharaj]

In article

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq,
implication 3.5.3 and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that
little effort is required. It means that the claim can be
understood, provided that the reader understands the text
thoroughly, but this thorough understanding typically
requires time and effort. In other words, the author is
trying to reassure the reader that to "see" the truth of
the claim, the text is sufficient, and other theorems and
texts are not required.
But none of this is easy, and I wonder whether students
might not realise that "easy" is being used in a slightly
atypical way, and worry unneccessarily if seeing something
"easy" takes them several hours.
Maybe "straightforward to see" would be more accurate
perhaps, because the process of understanding the text is
straightforward (but not easy).
Any opinions?
Paul

Consider "easy to see" to be encouragement.

Jai Maharaj, Jyotishi
Om Shanti
http://groups.google.com/group/alt.fan.jai-maharaj

[Athel Cornish-Bowden]

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that
the reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying to reassure
the reader that to "see" the truth of the claim, the text is sufficient,
and other theorems and texts are not required.
But none of this is easy, and I wonder whether students might not realise
that "easy" is being used in a slightly atypical way, and worry unneccessarily
if seeing something "easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps, because the
process of understanding the text is straightforward (but not easy).
Any opinions?

Yes, I have an opinion, which is that it is plain wrong to use "easy"
in a textbook with a specialized meaning different from how "easy" is
used in ordinary English. I was sufficiently irritated by this
expression half a century ago that I resolved that I would never say
"easy" in a textbook unless I was totally convinced that the thing in
question really was easy to see. I have kept this resolution, though
over the years I have modified my ideas of what is easy, as I realized
more and more that things that seem easy to me are not necessarily
perceived as easy by readers.

Someone commented on R. A. Fisher's* use of the expression "it is easy
to see" that something that Fisher found easy to see would usually
require two hours of hard work for an ordinary reader to see.

In "Surely you're joking, Mr Feynman" Richard Feynman discussed the
habit of mathematicians to say that any result was trivial, meaning
that it had been demonstrated to their satisfaction. One of them would
say that something was trivial, and there would follow two hours of
argument followed by general admission that it was indeed trivial.

*One of the greatest geneticists of the 20th century, and one of the
founders of the "modern synthesis" of Darwinian evolution and Mendelian
genetics. Difficult as it is to believe today, there was a strong
current of thought during the first quarter of the century that Mendel
made Darwin obsolete.

[J. J. Lodder]

Post by Athel Cornish-Bowden

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that
the reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying to reassure
the reader that to "see" the truth of the claim, the text is sufficient,
and other theorems and texts are not required.
But none of this is easy, and I wonder whether students might not
realise that "easy" is being used in a slightly atypical way, and worry
unneccessarily if seeing something "easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps, because
the process of understanding the text is straightforward (but not easy).
Any opinions?

Yes, I have an opinion, which is that it is plain wrong to use "easy"
in a textbook with a specialized meaning different from how "easy" is
used in ordinary English. I was sufficiently irritated by this
expression half a century ago that I resolved that I would never say
"easy" in a textbook unless I was totally convinced that the thing in
question really was easy to see. I have kept this resolution, though
over the years I have modified my ideas of what is easy, as I realized
more and more that things that seem easy to me are not necessarily
perceived as easy by readers.

It is a set form, at least in mathematics.
And if used right the thing in question really is easy to see,
once one has seen it.
The origin seems to have been Lagrange, in the 18th century,
who used 'on voit aisément' a lot in his works.
Standard reader response is groan and keep the aspirin bottle at hand.
But legend has it that Lagrange himself once needed a full week
to see one of his easies that he had forgotten once again.

The form is often abused however.
Einstein for example accused Hilbert
of having a 'superman complex', (Uebermensch komplex)
that is,
deliberately leaving out many intermediate steps from a derivation,
while pretending that these are immediately obvious
to a man of his immense genius.

They were not friends,

[grabber]

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that
the reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying to reassure
the reader that to "see" the truth of the claim, the text is sufficient,
and other theorems and texts are not required.
But none of this is easy, and I wonder whether students might not realise
that "easy" is being used in a slightly atypical way, and worry unneccessarily
if seeing something "easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps, because the
process of understanding the text is straightforward (but not easy).
Any opinions?
Paul

Raymond Smullyan had some anecdotes about the way maths professors used
the word "obvious".

In one of them, a professor remarks during a lecture that a proposition
is "obvious". When a student asks *why* it is obvious, the professor
goes into a trance and leaves the lecture room for ten minutes. Then he
comes back, says "Yes, it *is* obvious," and carries on with the lecture.

[David Kleinecke]

Post by grabber

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that
the reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying to reassure
the reader that to "see" the truth of the claim, the text is sufficient,
and other theorems and texts are not required.
But none of this is easy, and I wonder whether students might not realise
that "easy" is being used in a slightly atypical way, and worry unneccessarily
if seeing something "easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps, because the
process of understanding the text is straightforward (but not easy).
Any opinions?
Paul

Raymond Smullyan had some anecdotes about the way maths professors used
the word "obvious".
In one of them, a professor remarks during a lecture that a proposition
is "obvious". When a student asks *why* it is obvious, the professor
goes into a trance and leaves the lecture room for ten minutes. Then he
comes back, says "Yes, it *is* obvious," and carries on with the lecture.

The problem with many mathematical "obvious"s is that the
step called obvious really is obvious - if you have the
correct point-of-view. But there are many POVs in mathematics
and even the best mathematician may be in the wrong context.
Students more often than not don't have any mathematical POV.

[RH Draney]

Post by grabber
Raymond Smullyan had some anecdotes about the way maths professors used
the word "obvious".
In one of them, a professor remarks during a lecture that a proposition
is "obvious". When a student asks *why* it is obvious, the professor
goes into a trance and leaves the lecture room for ten minutes. Then he
comes back, says "Yes, it *is* obvious," and carries on with the lecture.

Wienerlore!...r

[Jerry Friedman]

Post by RH Draney

Post by grabber
Raymond Smullyan had some anecdotes about the way maths professors
used the word "obvious".
In one of them, a professor remarks during a lecture that a
proposition is "obvious". When a student asks *why* it is obvious, the
professor goes into a trance and leaves the lecture room for ten
minutes. Then he comes back, says "Yes, it *is* obvious," and carries
on with the lecture.

Wienerlore!...r

Yes, I tell my students that story with Wiener as the hero, and
sometimes add that I pick him rather than any other possibility because
I like saying "Norbert Wiener".

I also tell this one:

Wiener: Do you remember which way I was going before we started our
conversation?

Other mathematician, bemused: You were going that way.

Wiener: Good, then I /have/ had lunch.

[Richard Yates]

On Fri, 8 Jun 2018 09:03:11 -0600, Jerry Friedman

Post by Jerry Friedman

Post by RH Draney

Post by grabber
Raymond Smullyan had some anecdotes about the way maths professors
used the word "obvious".
In one of them, a professor remarks during a lecture that a
proposition is "obvious". When a student asks *why* it is obvious, the
professor goes into a trance and leaves the lecture room for ten
minutes. Then he comes back, says "Yes, it *is* obvious," and carries
on with the lecture.

Wienerlore!...r

Yes, I tell my students that story with Wiener as the hero, and
sometimes add that I pick him rather than any other possibility because
I like saying "Norbert Wiener".
Wiener: Do you remember which way I was going before we started our
conversation?
Other mathematician, bemused: You were going that way.

"Bemused" is bedeviling me these days.

Some dictionaries just ignore the, it seems to me, increasing trend
for it to be used to mean "wryly amused" rather than "confused or
perplexed" and list only the latter.

AHD online lists it as definition #3 and notes prominently that there
is a 'Usage Problem'.

M-W online includes it as definition #3 without any such comment.

The problem is that context almost always provides no clue, as in the
above example. The other mathematician might reasonably have been
perplexed _or_ wryly amused.

I find myself more bemused by it these days than bemused.

[Peter T. Daniels]

Post by Richard Yates
On Fri, 8 Jun 2018 09:03:11 -0600, Jerry Friedman

Post by Jerry Friedman

Post by RH Draney

Post by grabber
Raymond Smullyan had some anecdotes about the way maths professors
used the word "obvious".
In one of them, a professor remarks during a lecture that a
proposition is "obvious". When a student asks *why* it is obvious, the
professor goes into a trance and leaves the lecture room for ten
minutes. Then he comes back, says "Yes, it *is* obvious," and carries
on with the lecture.

Wienerlore!...r

Yes, I tell my students that story with Wiener as the hero, and
sometimes add that I pick him rather than any other possibility because
I like saying "Norbert Wiener".
Wiener: Do you remember which way I was going before we started our
conversation?
Other mathematician, bemused: You were going that way.

"Bemused" is bedeviling me these days.
Some dictionaries just ignore the, it seems to me, increasing trend
for it to be used to mean "wryly amused" rather than "confused or
perplexed" and list only the latter.
AHD online lists it as definition #3 and notes prominently that there
is a 'Usage Problem'.
M-W online includes it as definition #3 without any such comment.

M-W doesn't do "Problems." AHD was, at least originally, promoted as the
prescriptive alternative to the licentious M-W Third International.

Post by Richard Yates
The problem is that context almost always provides no clue, as in the
above example. The other mathematician might reasonably have been
perplexed _or_ wryly amused.
I find myself more bemused by it these days than bemused.

[J. J. Lodder]

Post by Jerry Friedman

Post by RH Draney

Post by grabber
Raymond Smullyan had some anecdotes about the way maths professors
used the word "obvious".
In one of them, a professor remarks during a lecture that a
proposition is "obvious". When a student asks *why* it is obvious, the
professor goes into a trance and leaves the lecture room for ten
minutes. Then he comes back, says "Yes, it *is* obvious," and carries
on with the lecture.

Wienerlore!...r

Yes, I tell my students that story with Wiener as the hero, and
sometimes add that I pick him rather than any other possibility because
I like saying "Norbert Wiener".
Wiener: Do you remember which way I was going before we started our
conversation?
Other mathematician, bemused: You were going that way.
Wiener: Good, then I /have/ had lunch.

Legend has it that there was a math professor who was so distraught
thet he couldn't go through a revolving door
with a better than 50% chance of ending up inside,

Jan

[Jack]

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that
the reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying to reassure
the reader that to "see" the truth of the claim, the text is sufficient,
and other theorems and texts are not required.
But none of this is easy, and I wonder whether students might not realise
that "easy" is being used in a slightly atypical way, and worry unneccessarily
if seeing something "easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps, because the
process of understanding the text is straightforward (but not easy).

Evident?

[s***@my-deja.com]

Post by Paul
Mathematics texts aimed at undergraduates or graduates
often use the phrase "easy to see".
"It is easy to see that with this definition of Eq,
implication 3.5.3 and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean
that little effort is required. It means that the
claim can be understood, provided that the reader
understands the text thoroughly, but this thorough
understanding typically requires time and effort.
In other words, the author is trying to reassure
the reader that to "see" the truth of the claim,
the text is sufficient, and other theorems and texts
are not required.
But none of this is easy, and I wonder whether students
might not realise that "easy" is being used in a slightly
atypical way, and worry unnecessarily if seeing something
"easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps,
because the process of understanding the text is
straightforward (but not easy).
Any opinions? Paul

"It can be seen"
"It can be deducted"

[Kerr-Mudd,John]

Post by s***@my-deja.com

Post by Paul
Mathematics texts aimed at undergraduates or graduates
often use the phrase "easy to see".
"It is easy to see that with this definition of Eq,
implication 3.5.3 and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean
that little effort is required. It means that the
claim can be understood, provided that the reader
understands the text thoroughly, but this thorough
understanding typically requires time and effort.
In other words, the author is trying to reassure
the reader that to "see" the truth of the claim,
the text is sufficient, and other theorems and texts
are not required.
But none of this is easy, and I wonder whether students
might not realise that "easy" is being used in a slightly
atypical way, and worry unnecessarily if seeing something
"easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps,
because the process of understanding the text is
straightforward (but not easy).
Any opinions? Paul

"It can be seen"
"It can be deducted"

"deduced" maybe. Deducted means taking it away.

[s***@my-deja.com]

Post by Kerr-Mudd,John

Post by s***@my-deja.com

Post by Paul
Mathematics texts aimed at undergraduates or graduates
often use the phrase "easy to see".
"It is easy to see that with this definition of Eq,
implication 3.5.3 and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean
that little effort is required. It means that the
claim can be understood, provided that the reader
understands the text thoroughly, but this thorough
understanding typically requires time and effort.
In other words, the author is trying to reassure
the reader that to "see" the truth of the claim,
the text is sufficient, and other theorems and texts
are not required.
But none of this is easy, and I wonder whether students
might not realise that "easy" is being used in a slightly
atypical way, and worry unnecessarily if seeing something
"easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps,
because the process of understanding the text is
straightforward (but not easy).
Any opinions? Paul

"It can be seen"
"It can be deducted"

"deduced" maybe. Deducted means taking it away.

You are right of course. "It can be deduced"

[J. J. Lodder]

Post by s***@my-deja.com

Post by Paul
Mathematics texts aimed at undergraduates or graduates
often use the phrase "easy to see".
"It is easy to see that with this definition of Eq,
implication 3.5.3 and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean
that little effort is required. It means that the
claim can be understood, provided that the reader
understands the text thoroughly, but this thorough
understanding typically requires time and effort.
In other words, the author is trying to reassure
the reader that to "see" the truth of the claim,
the text is sufficient, and other theorems and texts
are not required.
But none of this is easy, and I wonder whether students
might not realise that "easy" is being used in a slightly
atypical way, and worry unnecessarily if seeing something
"easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps,
because the process of understanding the text is
straightforward (but not easy).
Any opinions? Paul

"It can be seen"
"It can be deducted"

I never managed to deduct duct tape, once it had ducted,

Jan

[Madrigal Gurneyhalt]

Post by J. J. Lodder

Post by s***@my-deja.com

Post by Paul
Mathematics texts aimed at undergraduates or graduates
often use the phrase "easy to see".
"It is easy to see that with this definition of Eq,
implication 3.5.3 and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean
that little effort is required. It means that the
claim can be understood, provided that the reader
understands the text thoroughly, but this thorough
understanding typically requires time and effort.
In other words, the author is trying to reassure
the reader that to "see" the truth of the claim,
the text is sufficient, and other theorems and texts
are not required.
But none of this is easy, and I wonder whether students
might not realise that "easy" is being used in a slightly
atypical way, and worry unnecessarily if seeing something
"easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps,
because the process of understanding the text is
straightforward (but not easy).
Any opinions? Paul

"It can be seen"
"It can be deducted"

I never managed to deduct duct tape, once it had ducted,

It is not considered good conduct to conduct electricity via a
good conductor if the good conductor is conducting an
orchestra.

[Ken Blake]

On Fri, 8 Jun 2018 03:11:38 -0700 (PDT), Madrigal Gurneyhalt

Post by J. J. Lodder
I never managed to deduct duct tape, once it had ducted,

After years of believing that everyone who said "duck tape" instead of
"duct tape" was wrong, a few years ago I read somewhere (I can't
remember where) that it's actually "duck tape," or at least originally
was. The name comes from soldiers who used that kind of tape to seal
their boots and ammunition boxes against water.

Is this correct, or is it something else I believe in error.

[Madrigal Gurneyhalt]

Post by Ken Blake
On Fri, 8 Jun 2018 03:11:38 -0700 (PDT), Madrigal Gurneyhalt

Post by J. J. Lodder
I never managed to deduct duct tape, once it had ducted,

After years of believing that everyone who said "duck tape" instead of
"duct tape" was wrong, a few years ago I read somewhere (I can't
remember where) that it's actually "duck tape," or at least originally
was. The name comes from soldiers who used that kind of tape to seal
their boots and ammunition boxes against water.
Is this correct, or is it something else I believe in error.

You are both correct and incorrect and probably various stages in
between. I can only suggest that you read the Wiki article on duct
tape to get some idea of the can of worms you have opened.
Meanwhile, the fact that Duck Tape is a well known maker of duct
tape will suffice to indicate that the confusion is not one that any
one has any real interest in resolving!

[Ken Blake]

On Fri, 8 Jun 2018 08:56:14 -0700 (PDT), Madrigal Gurneyhalt

Post by Madrigal Gurneyhalt

Post by Ken Blake
On Fri, 8 Jun 2018 03:11:38 -0700 (PDT), Madrigal Gurneyhalt

Post by J. J. Lodder
I never managed to deduct duct tape, once it had ducted,

After years of believing that everyone who said "duck tape" instead of
"duct tape" was wrong, a few years ago I read somewhere (I can't
remember where) that it's actually "duck tape," or at least originally
was. The name comes from soldiers who used that kind of tape to seal
their boots and ammunition boxes against water.
Is this correct, or is it something else I believe in error.

You are both correct and incorrect and probably various stages in
between. I can only suggest that you read the Wiki article on duct
tape to get some idea of the can of worms you have opened.
Meanwhile, the fact that Duck Tape is a well known maker of duct
tape will suffice to indicate that the confusion is not one that any
one has any real interest in resolving!

Thanks to everyone who replied.

[Richard Yates]

Post by Ken Blake
On Fri, 8 Jun 2018 03:11:38 -0700 (PDT), Madrigal Gurneyhalt

Post by J. J. Lodder
I never managed to deduct duct tape, once it had ducted,

After years of believing that everyone who said "duck tape" instead of
"duct tape" was wrong, a few years ago I read somewhere (I can't
remember where) that it's actually "duck tape," or at least originally
was. The name comes from soldiers who used that kind of tape to seal
their boots and ammunition boxes against water.
Is this correct, or is it something else I believe in error.

I heard that the term comes from "duck canvas" a heavy, plain woven
cotton fabric as this kind of cloth is/was the backing for duck tape.
Having already known the term "duck canvas", this story rang true for
me.

[Peter Duncanson [BrE]]

On Fri, 08 Jun 2018 09:09:43 -0700, Richard Yates

Post by Richard Yates

Post by Ken Blake
On Fri, 8 Jun 2018 03:11:38 -0700 (PDT), Madrigal Gurneyhalt

Post by J. J. Lodder
I never managed to deduct duct tape, once it had ducted,

After years of believing that everyone who said "duck tape" instead of
"duct tape" was wrong, a few years ago I read somewhere (I can't
remember where) that it's actually "duck tape," or at least originally
was. The name comes from soldiers who used that kind of tape to seal
their boots and ammunition boxes against water.
Is this correct, or is it something else I believe in error.

I heard that the term comes from "duck canvas" a heavy, plain woven
cotton fabric as this kind of cloth is/was the backing for duck tape.
Having already known the term "duck canvas", this story rang true for
me.

OED:

duck, n.3

Etymology: Known only from 17th cent.; apparently < 17th cent.
Dutch doeck ‘linnen or linnen cloath’ (Hexham 1678); = German tuch,
Icelandic dúkr, Swedish duk.

1. A strong untwilled linen (or later, cotton) fabric, lighter and
finer than canvas; used for small sails and men's (esp. sailors')
outer clothing.
In the earlier half of the 19th cent. much worn for trousers.

duck tape n. a strong adhesive tape made of waterproofed cotton
fabric (a proprietary name in the United States); cf. duct tape n.
at duct n. Additions.
In quot. 1899 the sense is apparently ‘a decorative strip of
duck’.
1899 Daily Picayune (New Orleans) 8 Feb. 3/5 In the washable
suits for later wear pique and duck tape take the lead, especially
in white and dark blue.
1902 Brooklyn Daily Eagle 21 Nov. 15/2 Considering..that 100,000
yards of cotton duck tape must be wrapped around the cable [of the
Williamsburg bridge] with neatness and exactitude, it may be
imagined that this method of cable preservation is quite
expensive.
....

duct tape n. [perhaps an alteration of earlier duck tape n. at
duck n.3 Additions] orig. N. Amer. a strong cloth-backed waterproof
adhesive tape, originally used for sealing joints in heating and
ventilation ducts, and (later) for holding electrical cables
securely in place, now in widespread general use esp. to repair,
secure, or connect a range of appliances, fixtures, and equipment;
cf. gaffer tape n. at gaffer n. Additions.

gaffer tape n. (also gaffa tape, gaffer's tape) [after use of the
tape by electricians for holding electrical cables securely in
place] a strong, cloth-backed, waterproof, adhesive tape (cf. duck
tape n. at duck n.3 Additions, duct tape n. at duct n. Additions).

[J. J. Lodder]

Post by Peter Duncanson [BrE]
On Fri, 08 Jun 2018 09:09:43 -0700, Richard Yates

Post by Richard Yates

Post by Ken Blake
On Fri, 8 Jun 2018 03:11:38 -0700 (PDT), Madrigal Gurneyhalt

Post by J. J. Lodder
I never managed to deduct duct tape, once it had ducted,

After years of believing that everyone who said "duck tape" instead of
"duct tape" was wrong, a few years ago I read somewhere (I can't
remember where) that it's actually "duck tape," or at least originally
was. The name comes from soldiers who used that kind of tape to seal
their boots and ammunition boxes against water.
Is this correct, or is it something else I believe in error.

I heard that the term comes from "duck canvas" a heavy, plain woven
cotton fabric as this kind of cloth is/was the backing for duck tape.
Having already known the term "duck canvas", this story rang true for
me.

duck, n.3
Etymology: Known only from 17th cent.; apparently < 17th cent.
Dutch doeck 'linnen or linnen cloath' (Hexham 1678); = German tuch,
Icelandic dúkr, Swedish duk.
1. A strong untwilled linen (or later, cotton) fabric, lighter and
finer than canvas; used for small sails and men's (esp. sailors')
outer clothing.
In the earlier half of the 19th cent. much worn for trousers.

Still in use. Modern Dutch spelling 'doek', also in 'zeildoek'.
Used for sails, and when waxed or oiled also for waterproofed clothing.
(obsolete)
Also 'opdoeken', to fold and bind sails to the spars.
Figuratively used for: to get rid of, to discontinue (of a business)

Also used for paintings, 'een doek van Rembrandt',

Jan

[J. J. Lodder]

Post by Richard Yates

Post by Ken Blake
On Fri, 8 Jun 2018 03:11:38 -0700 (PDT), Madrigal Gurneyhalt

Post by J. J. Lodder
I never managed to deduct duct tape, once it had ducted,

After years of believing that everyone who said "duck tape" instead of
"duct tape" was wrong, a few years ago I read somewhere (I can't
remember where) that it's actually "duck tape," or at least originally
was. The name comes from soldiers who used that kind of tape to seal
their boots and ammunition boxes against water.
Is this correct, or is it something else I believe in error.

I heard that the term comes from "duck canvas" a heavy, plain woven
cotton fabric as this kind of cloth is/was the backing for duck tape.
Having already known the term "duck canvas", this story rang true for
me.

'Linnen', (E. Linen) originaly, for better strength,
nowadays perhaps 'Kevlar doek',

Jan

[Jerry Friedman]

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that
the reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying to reassure
the reader that to "see" the truth of the claim, the text is sufficient,
and other theorems and texts are not required.
But none of this is easy, and I wonder whether students might not realise
that "easy" is being used in a slightly atypical way, and worry unneccessarily
if seeing something "easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps, because the
process of understanding the text is straightforward (but not easy).
Any opinions?

"It follows"? "It can be shown"? "The reader should verify"?

[Pavel Svinchnik]

Post by Jerry Friedman

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that
the reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying to reassure
the reader that to "see" the truth of the claim, the text is sufficient,
and other theorems and texts are not required.
But none of this is easy, and I wonder whether students might not realise
that "easy" is being used in a slightly atypical way, and worry unneccessarily
if seeing something "easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps, because the
process of understanding the text is straightforward (but not easy).
Any opinions?

"It follows"? "It can be shown"? "The reader should verify"?
--
Jerry Friedman

I have my degrees in Mathematics and during my student days found the phrase "the proof of which is left as an exercise to the reader" quite annoying.


Paul

[RH Draney]

Post by Pavel Svinchnik

Post by Jerry Friedman
"It follows"? "It can be shown"? "The reader should verify"?

I have my degrees in Mathematics and during my student days found the phrase "the proof of which is left as an exercise to the reader" quite annoying.

"I have discovered a truly remarkable proof of this theorem which this
margin is too small to contain."

....r

[Kerr-Mudd,John]

Post by RH Draney

Post by Pavel Svinchnik

Post by Jerry Friedman
"It follows"? "It can be shown"? "The reader should verify"?

I have my degrees in Mathematics and during my student days found the
phrase "the proof of which is left as an exercise to the reader"
quite annoying.

"I have discovered a truly remarkable proof of this theorem which this
margin is too small to contain."
....r

Not /quite/ obvious then. Larger margins have been tried, but it wasn't
easy.

https://en.wikipedia.org/wiki/Andrew_Wiles#Proof_of_Fermat's_Last_Theorem

[Richard Tobin]

Post by Pavel Svinchnik
I have my degrees in Mathematics and during my student days found the
phrase "the proof of which is left as an exercise to the reader" quite
annoying.

When I ran out of time during an exam I wrote "left as an exercise for
the examiner".

-- Richard

[Peter Moylan]

Post by Pavel Svinchnik
I have my degrees in Mathematics and during my student days found the
phrase "the proof of which is left as an exercise to the reader"
quite annoying.

Many of those make good student exercises.

At the beginning of my third undergraduate year, I was asked to explain,
as part of a large assignment, why the theorem that any integer has a
unique factorisation into prime factors failed for some integral
domains. (I don't guarantee that that last part is right. My memory
isn't that good.) My conclusion was that the textbook proof also failed
for the natural numbers. After much struggling, I finally pinned down
where the textbook proof used a circular argument.

That was probably why I passed that assignment, which counted for a
third of the subject. But I ended up dropping the subject anyway,
because of excessive workload.

[J. J. Lodder]

Post by Paul
Mathematics texts aimed at undergraduates or graduates often use
the phrase "easy to see".
"It is easy to see that with this definition of Eq, implication 3.5.3
and equivalence 3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little effort
is required. It means that the claim can be understood, provided that the
reader understands the text thoroughly, but this thorough understanding
typically requires time and effort. In other words, the author is trying
to reassure the reader that to "see" the truth of the claim, the text is
sufficient, and other theorems and texts are not required.
But none of this is easy, and I wonder whether students might not realise
that "easy" is being used in a slightly atypical way, and worry
unneccessarily if seeing something "easy" takes them several hours.
Maybe "straightforward to see" would be more accurate perhaps, because the
process of understanding the text is straightforward (but not easy).
Any opinions?

'One easily sees' should be understood as 'there is an easy way to see',

Jan

[Peter Moylan]

Mathematics texts aimed at undergraduates or graduates often use the
phrase "easy to see". Here's a typical example: "It is easy to see
that with this definition of Eq, implication 3.5.3 and equivalence
3.5.4 are valid..."
However, the word "easy" in this context doesn't mean that little
effort is required. It means that the claim can be understood,
provided that the reader understands the text thoroughly, but this
thorough understanding typically requires time and effort. In other
words, the author is trying to reassure the reader that to "see" the
truth of the claim, the text is sufficient, and other theorems and
texts are not required.
But none of this is easy, and I wonder whether students might not
realise that "easy" is being used in a slightly atypical way, and
worry unneccessarily if seeing something "easy" takes them several
hours.
Maybe "straightforward to see" would be more accurate perhaps,
because the process of understanding the text is straightforward (but
not easy).
Any opinions?

I have preferred "It is obvious that ...".

I've been caught by this, though. On one occasion I claimed that
something was obvious, and when challenged (by myself, as it happened)
it took me two years to re-derive the proof.

I was right, though. Once I had the proof, I could see that it was obvious.