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bio website andrej.com
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visits member for 2 years, 8 months
seen Jan 6 at 23:28

Jan
6
revised How to introduce type theory to newcomer
added 1209 characters in body
Jan
6
answered How to introduce type theory to newcomer
Dec
27
comment Geometric Series Word Problem from Khan Academy
You won't learn anything by getting all the answers. Figure it out by yourself. Once you are convinced that you know what is right, come back to check. (By "convinced" I mean that you won't just immediately assume you're wrong if my answer is different from yours.)
Dec
27
comment Geometric Series Word Problem from Khan Academy
It's about an off-by-one error: to add the first ten terms of the series, should you plug in $n = 9$, $n = 10$, or $n = 11$? The answer depends on how you start indexing the series, i.e., if the first term corresponds to $n = 0$ then you should plug in $n = 9$ to get ten terms. However, if you start counting terms with $n = 1$ then you should plug in $n = 10$. This error is so prevalent in programming that it has a name: "Obi-Wan error".
Dec
27
revised Geometric Series Word Problem from Khan Academy
added 12 characters in body
Dec
27
answered Geometric Series Word Problem from Khan Academy
Dec
27
comment Question about how to prove $x^5\equiv x \pmod {10}$
What's wrong with churning out the 10 cases by brute force?
Dec
18
comment Give the explicit form of the following parametrized surface
I mean that I disagree with my answer.
Dec
18
comment Give the explicit form of the following parametrized surface
Hmm, this can't be right.
Dec
18
answered Give the explicit form of the following parametrized surface
Dec
8
awarded  Caucus
Dec
4
comment Correspondence between two subspaces
Amazingly, we came up with the same notation (it's not suprising that we came up with the same proof).
Dec
4
answered Correspondence between two subspaces
Sep
30
awarded  Explainer
Aug
30
comment How to prove that a set is infinite iff it is Dedekind infinite?
Also, there are infnite sets $X$ such that there is no bijection from $\mathbb{N}$ to $X$. These are called uncountable. I don't know how much you already know, perhaps you already knew that.
Aug
30
comment How to prove that a set is infinite iff it is Dedekind infinite?
If $X$ is countably infinite then of course there is a bijection $b : \mathbb{N} \to X$ (by definition of "countably infinite"), but the proof of Proposition 1 need not produce such a bijection: it could happen that the $i$ we get from the proof is not surjective, even though some other map $b : \mathbb{N} \to X$ is surjective.
Aug
28
comment Models of set theory
I wrote a shorter answer here as well.
Aug
28
answered Models of set theory
Aug
28
comment Models of set theory
Perhaps the gist of my answer was the last sentence: if you ask "why are model theorists justified in using sets?" then I ask back "why are number theorists justified in using numbers?"
Aug
28
comment Models of set theory
A similar question was asked on MathOverflow, which I answered at length: mathoverflow.net/questions/23060/set-theory-and-model-theory/… I recommend the answer :-)