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14h
comment What is the similarity between the numbers $85, 19,17, 4$ and $2$?
None of them is equal to 48.
Feb
3
comment Why every fundamental group isn't a trivial fundamental group?
@Trevor Topologists also use the term “torus” for any product of one or more circles $S^1\times S^1\times\dots \times S^1$. This includes $S^1$ itself as well as the standard 2-torus $S^1\times S^1$.
Feb
3
comment Book on foundational reasoning of standard arithmetics “curriculum”
That's “Bertrand Russell”.
Feb
3
comment How to find $x$ when $2^{x}+3^{x}=6$?
What does “stiff” mean?
Feb
1
comment What is the denial of a statement in logic math?
Any sentence can be negated by appending “It is not the case that” to the beginning. For example, the negation of “Some people are honest and some people are not honest” is “It is not the case that some people are honest and some people are not honest.”
Feb
1
comment Definition of “well defined” in mathematics
What are well-defined functions?
Jan
31
comment What are the units in $\mathbb{Z}/n\mathbb{Z}$ in general?
$m$ is a unit in $\Bbb Z/n\Bbb Z$ if and only if $m$ and $n$ are relatively prime. To prove this solve Bézout’s equation $am+bn=1$.
Jan
30
comment Regular and context free language
Consider this: Let $P$ be the set of prime numbers other than 2: $\{3,5,7,11,13,17,19,23,\ldots\}$. Let $O$ be the set of odd numbers. It's easy to recognize members of $O$; just look at the last digit. Recognizing members of $P$ is difficult, even though $P$ is a subset of $O$. Or let $X$ be the set of Americans and let $Y$ be the set of Americans who would do a good job if elected President. Members of $X$ are easy to recognize, members of $Y$ much less so.
Jan
30
comment Is the sequence $0,1,0,0,1,0,0,0,1,0,0,0,0,1,\ldots$ convergent?
If it were convergent, what would be its limit?
Jan
29
comment Find the minimal polynomial of the number $\sqrt{2} + \sqrt{3}$ on $\mathbb{Q}$ and on $\mathbb{Q}\sqrt{2}$
Related: Constructing a degree 4 rational polynomial satisfying $f(\sqrt{2}+\sqrt{3}) = 0$
Jan
25
comment Placing stones on vertices of polygon
I wrote a blog post with a detailed analysis of this game.
Jan
23
comment Why does an argument similiar to 0.999…=1 show 999…=-1?
Closely related: Divergent series and $p$-adics
Jan
23
comment Is it possible to have two difference (appropriate) universal sets for a collection of sets?
The system in Whitehead and Russell's Principia Mathematica has more than one universal set; it has an infinite hierarchy of universal sets.
Jan
21
comment Counting the Number of Faces on A Soccer Ball
This search finds several relevant posts.
Jan
21
comment Counting the Number of Faces on A Soccer Ball
I hope this isn't unhelpful, but as stated, the thing you want to prove is false. The number of hexagons can vary. For example, a standard soccer ball has 20 hexagons, but a pentagonal dodecahedron (which also satisfies the definition of “soccer ball” that you gave) has 0 hexagons. Many other examples exist.
Jan
19
comment What's the official name for a space that warps like this?
Pac-man might be on a torus. We don't have enough evidence to rule it out. :)
Jan
12
comment Negation of injectivity
Your problem is that you have translated "but" as $\implies$ when it should be $\land\lnot$.
Jan
12
comment Using induction for an easy proof for formal languages
Does $(w)_i$ mean the i'th symbol in $w$?
Jan
7
comment Elementary books by good mathematicians
Yes, or I would not have mentioned it.
Jan
5
comment Can there be a single game of Chess which includes all the possible situations that may arise during Chess?
No, because some games end with a king against king and rook, and other games end with a king against king and bishop, and there is no way to get from one to the other.