2,448 reputation
1527
bio website math.berkeley.edu/~sramesh
location Berkeley, CA
age 30
visits member for 5 years, 5 months
seen 6 hours ago

I was a graduate student in the Logic program at Berkeley, broadly interested in categorical logic and foundations of mathematics, as well as in applications of category theory to the semantics of programming languages. I work for Google now.


Aug
15
awarded  Nice Answer
Aug
2
comment Are all the theorems true?
(I suppose I should point out, in case you are not aware, that the reason ZFC + "ZFC is inconsistent" is equiconsistent with ZFC is because of Goedel's second incompleteness theorem)
Aug
2
comment Are all the theorems true?
The example I gave is also not restricted to PA. It works in exactly the same way for any base theory capable of speaking of itself; e.g., if ZFC is consistent, then ZFC + "ZFC is inconsistent" is consistent but not "good".
Aug
2
comment Are all the theorems true?
If question 3 is restricted to theories which are "good", then of course they will be consistent as well... consistency is part of your definition of "goodness"! What could question 3 be asking about, if not the question of whether there is a consistent, non-"good" theory?
Aug
1
answered Are all the theorems true?
Jul
10
comment Fiction books about mathematicians?
Mathematicians should not do, and certainly not enjoy, anything other than mathematical research, lest they give themselves away as human beings with a variety of interests and not a 100% devotion to just the one.
Jun
16
comment Ingenuity in mathematics
[Pedantic note: 0 and n - 1 can both occur if there is only 1 person at the party. But perhaps it is implicit in "party" that there are at least two people.]
Jun
9
comment What are good non-English languages for mathematicians to know?
Knowing some programming language well is probably useful. But C, specifically, needn't be it...
Jun
1
comment Is complement of LL(k) grammar context free?
en.wikipedia.org/wiki/LL_parser
May
23
awarded  Enlightened
May
23
awarded  Nice Answer
May
2
comment existence of a field that has a non surjective ring homomorphism
I usually leave only comments rather than answers, to bypass the silly reputation system. But for once, I thought, let me post an actual answer. And what's the result? A bunch of responses about somebody else's answer-posted-as-comment. :)
May
2
comment existence of a field that has a non surjective ring homomorphism
Ah, good point! I should have thought of that. I kept implicitly thinking $\mathbb{R}$ was algebraically closed...
May
2
revised existence of a field that has a non surjective ring homomorphism
D'oh!
May
2
answered existence of a field that has a non surjective ring homomorphism
Apr
9
comment Why the underlying function of a monomorphism may not be an injection
What more are you looking for, beyond "A generalization may not always behave exactly the same as the thing it generalized, in all respects"? For what it's worth, in the quite common case of a concrete category in which the underlying set functor is representable, (i.e., in which there is a free object on one element), all monomorphisms will be injections. In some sense, the failure of monomorphisms to be injections more generally is just the failure of the underlying set functor to always be representable.
Feb
19
comment Nontrivial question about Fibonacci numbers?
Tilings using 1x1 and 1x2 tiles? Bah! It's a direct observation that the "right parents" of each diagonal comprise the previous diagonal, while the "left parents" comprise the twice-previous diagonal.
Feb
12
comment Covering the Rationals — A Paradox?
So the problem is mainly your second bullet point, but it does not involve a new uncountable infinity (and what would it mean to be an uncountable infinity smaller than $\aleph_0$?). You are simply wrong in supposing that the number of gaps will be less than the number of rationals; you have no means of constructing a partial surjection from the latter to the former.
Feb
12
comment Covering the Rationals — A Paradox?
Indeed, instead of using mini-intervals, we might imagine removing single points: removing one rational at a time from [0, 1], we end up with n + 1 many connected components left after the first n many rationals have been removed. But after removing every rational, we are not left with a countable collection of connected components; instead, we are left with an uncountable collection of single points (the irrationals).
Feb
12
comment Covering the Rationals — A Paradox?
It is not true that the number of gaps must be countable. Your argument is simply "The number of gaps when the first n mini-intervals have been placed is <= n + 1; therefore, the number of gaps when all the mini-intervals have been placed is countable". But this argument is fallacious.