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2d
comment Why do we classify infinities in so many symbols and ideas?
"the set of all possible problems you might want a computer program to solve is strictly bigger (cardinality of ℝ)" Oh, I want to solve many more problems than the cardinality of R ... ;)
Mar
2
comment Correct set notation for “all integers which are not multiples of 7”?
Isn't this almost the same as the first line in the question?
Feb
29
comment Are there arbitrarily large gaps between consecutive primes?
And I think it can probably be improved even further (for n>=4) by not using LCM but the product of all primes <= n+1.
Feb
29
comment Are there arbitrarily large gaps between consecutive primes?
Everyone knows the (n+1)! + k (with 2<=k<=n+1) example. We can actually use the lower (n+1)! - k or even better the much lower LCM(2, 3, ..., n+1) - k. For n=3, we get LCM(2,3,4)=12 and the numbers are 10,9,8. For n=5 we get LCM(2, ..., 6)=60 and the numbers are 58,57,56,55,54.
Feb
17
comment Prove the following trigonometric identity without a calculator involved
Proving only with a calculator would be harder ;)
Jan
10
comment Does the set of all fields exist ?
(just a comment, related to the last paragraph): If we restrict to ordered fields, there are also the Surreal numbers Field (and the isomorphic maximal hyperreals Field) which contain all possible ordered fields as subfields. (Field instead of field because they are classes, not sets). See: Surreals
May
24
comment Compute $\lim_{n \to \infty} \left(\frac{1}{\sqrt{n^3+1}} + \frac{1}{\sqrt{n^3+4}} + \cdots + \frac{1}{\sqrt{n^3+n^2}}\right)$
@GregoryGrant you need to correct the answer. (the $n / \sqrt{n^3+n^2}$ to $n / \sqrt{n^3}$)
May
24
comment Compute $\lim_{n \to \infty} \left(\frac{1}{\sqrt{n^3+1}} + \frac{1}{\sqrt{n^3+4}} + \cdots + \frac{1}{\sqrt{n^3+n^2}}\right)$
@Gregory your inequality is wrong. $n / sqrt(n^3+n^2) > 1 / sqrt(n^3)$
May
9
comment Math problems that are impossible to solve
I agree with Gerry. I was considered a big surprise when - some thousands of years ago - they proved this, and therefore that there are irrational numbers.
Apr
29
comment How to construct a product set whose complement is not a product set?
Why not $A \times X \subset X \times X$ ?
Apr
6
comment Is There any formula to calculate automorphism with the spesific graph?
Dn x (Sk)^n where k = s-2 I'm not exactly sure about the group itself but the size of it is certainly 2n x (s-2)^n. Matches your 2x3x(3-2)^3=6 and 2x4x(3-2)^4=8
Apr
6
comment Is There any formula to calculate automorphism with the spesific graph?
The group seems to be D4 x (S2)^4
Apr
6
comment Inequality involving Square Root
The answer is correct but not the solution.
Mar
26
comment Seeking guide for project.
The "Knot Book" by Colin Adams is my favourite. You should definitely have a look at it if you can find it in the univ. library.
Jan
18
comment Why do some other people use dek and el rather than letters as the eleventh and twelfth digits in the dozenal or duodecimal system?
"deka" is the Greek word for ten. It looks closer to dek than decem.
Dec
18
comment Does this algorithm find prime numbers only?
" for verifying that 147 is prime, ..."? The wording does not look appropriate, considering that 147 is not prime.
Dec
13
comment Trisecting an angle
and another +1 for the conclusion that you must have made a mistake.
Dec
13
comment Trisecting an angle
An initial 135 degrees angle would also demonstrate the problem quite well. The resulting 3 angles would not be 45 degrees and it's easy to check visually (adding 2 of them would not be equal to 90 degrees)
Dec
8
comment Find value of sum of reciprocals of powers of a number
@Wood or x=1 (instead of 0.5)
Dec
4
comment Why is it that $f(x)$ is even if $f(-x) = f(x)$?
Definitions do not require proof. It's like baptizing. I baptized myself ypercube. Therefore ypercube is me. We baptized even functions all those functions f that satisfy f(x) = f(-x) for all x that f is defined.