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Jul
22
comment Why there is no sign of logic symbols in mathematical texts?
generally, Logical symbols are only used when talking about Logic: (mathematical logic, metamathematics, set theory, foundations, etc.). There are a variety of reasons for doing this, most having to do with readability and comprehension. For example, using symbols only for the subject expressions and using text for the logical/meta expressions minimizes the chance of confusing the two.
Jul
13
comment Why do we treat dot product like a square?
Because she's just not cool, man.
Jun
19
revised Are there fewer reals on $(0, 1)$ than on $(1,\infty)$?
added 4 characters in body
Jun
19
awarded  Teacher
Jun
19
revised Are there fewer reals on $(0, 1)$ than on $(1,\infty)$?
added 3 characters in body
Jun
19
comment Are there fewer reals on $(0, 1)$ than on $(1,\infty)$?
@AtulGangwar Yes, you are correct. It's been awhile for me, and Ive fallen into the habit of using CS terms. I will fix it, thanks.
Jun
19
answered Are there fewer reals on $(0, 1)$ than on $(1,\infty)$?
May
1
comment Why did mathematicians introduce the concept of uniform continuity?
To be clear, "practical application" and "application to a theorem" are completely different things.
Jan
11
comment Why are primes considered to be the “building blocks” of the integers?
For instance, you could formulate a "unique sum theorem" if you limited the "additive primes" to just the number one(1). This is not really very interesting nor useful as it merely restates what Peano's fifth(?) postulate already clearly implies. And there's no interesting structure or re-combination to a system consisting of a single prime only.
Jan
11
comment Why are primes considered to be the “building blocks” of the integers?
@MattGregory No, that's just it. There is no "unique sum theorem" known that is both interesting and useful, except those that are really just the Prime Factorization Theory(PFT) clumsily restated to avoid using multiplication. And since those are really PFT, they end up with the same "primes" as we have now. Same thing applies to powers.
Dec
4
comment Is there a shape with infinite area but finite perimeter?
Sure. An infinitely long cylinder has an infinite area, but a perimeter length of zero. Of course, that's not in $\mathbb{R}^2$, which was not stated as a requirement, but may have been intended..?
Sep
25
comment Is it true to say that “it's not logically possible to prove something can't be done”?
This is just a slightly smartened up version of the inane truism "You can't prove a Negative." Obviously not true in mathematics and formal system, but less obviously, not true in any common reasoning system that has a notion of "proof". What's really meant is "You can't prove a Universal.", at least not empirically. Scott Adams is brilliant, but he's definitely wrong on this one. Saying that you can't prove that anything can't be done is effectively equivalent to saying that you can't disprove anything.
Jul
28
revised Interview puzzle with a deck of cards, some cards upside-down
correcting opposite of upside down. (keep missing pieces)
Jul
28
suggested approved edit on Interview puzzle with a deck of cards, some cards upside-down
Jul
20
comment Elementary theorems with several proofs?
This probably should be a community wiki, since it does not have a single correct answer.
Apr
14
comment Limit is found using polar coordinates but it is not supposed to exist.
OMG, I will upvote you just for the images if you'll tell us what you used to make them...
Mar
30
comment Why would you expand a square wave in a Fourier series?
All modern digital audio uses the Fourier Transforms extensively, so knowing a square wave's Fourier series can be very helpful to understanding why, say, a hi or lo-pass filter changes its shape in various ways. learnabout-electronics.org/ac_theory/filters84.php
Mar
21
comment Why is $\sin^2x + \cos^2x = 1$ important?
$\sin^2x + \cos^2x = 1$ is basically just the Pythagorean identity ($a^2 + b^2 = c^2$) expressed in Trigonometric terms instead of Algebraic terms. And that's important because the Pythagorean theorem is the basis for almost all trigonometry.
Mar
18
revised If the infinite cardinals aleph-null, aleph-two, etc. continue indefinitely, is there any meaning in the idea of aleph-aleph-null?
Included theactual question into the body of the post.
Mar
18
comment If the infinite cardinals aleph-null, aleph-two, etc. continue indefinitely, is there any meaning in the idea of aleph-aleph-null?
FYI: make sure that your actual question is in the body of your post. It's confusing to have it only in the title.