Reputation
10,389
Next privilege 15,000 Rep.
Protect questions
Badges
1 20 47
Newest
 Nice Answer
Impact
~137k people reached

2d
comment Is university math all about proofs?
What you've explained here is not so much that mathematicians do more than just write proofs, just that writing a proof is a complex process. "Do painters just make paintings?" "No no, we first of all have to come up with the idea for what to paint, then worry about composition, then sketch the lineart..." "Why do you do all that?" "Well, to get a painting out of it." "Okay, so you do just make paintings."
2d
comment What does “2- place real function” mean?
You're going to have to include more context. It probably means a function mapping two real number inputs to a single real number output, though.
May
20
comment Is 'Algebraic Number Theory' the study of the theory of algebraic numbers, or is it the study of the theory of numbers from an algebraic viewpoint?
@ZevChonoles In other words, the name satisfies the law of associativity.
May
20
comment Proving the following number is real
The heart of it is: 1) to show that something is real, show that it equals its own conjugate, and 2) for numbers on the unit circle, the conjugate is the same as the inverse.
May
20
comment Can anyone help me solve this?
@Al3 Well, I left that unsolved deliberately. The key is that a tap pumps out the same volume of water every hour, so if you write $v$ for that volume, and $V$ is the volume of the pool, the pool will fill up in $V/v$ hours.
May
19
comment What is zero? Irrational or rational or it have both the properties?
Or less trivially, $2=\frac {\sqrt 8} {\sqrt 2}$
May
19
comment Decomposition for a Sum of Matrix Products
Is $X'$ the transpose?
May
18
comment What is meant by a stopping time?
You may find this question helpful.
May
18
comment Books that start with questions?
I remember coming across an introductory group theory book once that was literally nothing but questions (a textbook, not an exercise book), but I can't remember what it was called.
May
17
comment Is there active research in trigonometry?
What do you mean by "modern values"? Furthermore, the fact that a problem is unsolved doesn't mean it's being actively researched.
May
17
comment Is there active research in trigonometry?
@NasuSama You sure about that?
May
17
comment Trouble understanding what a measure-zero set is.
What exactly do you mean when you say you don't understand what this means? Do you at least know the definition of a zero-measure set?
May
16
comment Are there mathematical objects that have been proved to exist but cannot be described in words?
Not only do you need to specify what you mean by "described", you need to define "exists". The intuitionist point of view is that when we're talking about mathematical objects, if you can't describe it, it doesn't exist - that imaginary objects are only conjured into existence by our describing them explicitly. From that point of view, what you're looking for is impossible.
May
12
comment Theorem 1 in Khinchin's “Continued Fractions”
Yes, but the situation to which formula (6) is applied in the proof of Theorem 1 doesn't seem to be of that form.
May
12
comment What is the motivation for analytic solutions in Mathematical Physics?
@VladimirSotirov I suppose formulae are better viewed as a subset of quantitative knowledge rather than a different kind of knowledge altogether. It's true that if formulae didn't provide numerical output, they wouldn't be as interesting, because the foundation (maybe even the definition) of physics is the quantification of the natural world. Still, my fundamental point is correct: a formula is a distinct piece of knowledge, interesting in its own right, to a mere table of numbers, and not simply a tool to obtain such a table.
May
11
comment Precise meaning of “extension”?
You can basically replace "extension" by "members".
May
11
comment Need a counter example for cycle in a graph
The idea is that a graph contains no cycle if and only if it's a tree, in the common sense of the word tree as a graph that can be drawn as a series of branching paths terminating in leaves. The degree one vertices are precisely the leaves and the root, and a tree has at least one leaf, so with the root that's a minimum of two vertices of degree 1.
May
11
comment How do I prove this function is monotonic?
Monotonic only implies one-to-one if the function is continuous.
May
10
comment Why is this proof of $i = -1$ wrong?
@user86418 Fair enough, I was sensitive because of the very negative response this question is getting outside of your comment.
May
10
comment Why is this proof of $i = -1$ wrong?
@user86418 Which similar questions are these, and how do you propose the OP should have gone about finding them? Look up "false proof" and sift through the hundreds of questions in case one of them happens to be the exact same one as in this question?