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Mathematics professor at Cambridge

Nov
28
asked Typical value of totient function
Nov
28
revised Intuitive explanation to Probability question
added 42 characters in body
Nov
28
answered Intuitive explanation to Probability question
Nov
26
answered A random walk matrix has eigenvalue 1 with multiplicty 1 - why?
Nov
23
answered Finding the new zeros of a “perturbed” polynomial
Nov
23
awarded  Nice Answer
Nov
22
answered Ramsey Theory, monochromatic subgraphs
Nov
21
comment Can infinity shorten proofs a lot?
Not the latter as I go by my middle name. Happy to make the change but have not managed to find where I can do it. (Please excuse my utter incompetence.)
Nov
20
awarded  Commentator
Nov
20
comment Continued fractions using all natural integers
I think you're right -- and indeed I was worried that something like that would happen. So it seems that the quotients have to grow rather fast to make the number transcendental.
Nov
20
answered Continued fractions using all natural integers
Nov
20
answered Are there any good nonconstructive “existential metatheorems”?
Nov
19
awarded  Nice Answer
Nov
18
awarded  Nice Answer
Nov
18
answered Beamer hints and tips
Nov
18
answered What's so great about blackboards?
Nov
18
comment Can infinity shorten proofs a lot?
I'm not sure I count induction either. It seems to me that one is not relying on infinity in a serious way to sum the first million cubes: one is saying, "If it's valid for 1 then it's valid for 2, and if it's valid for 2 then it's valid for 3, and ... and if it's valid for 999999 then it's valid for 1000000." That is a ridiculously long proof, but induction allows one to shorten it by giving a rule for when it's OK to put in the "..." (A more formal way of making the point is that the axiom of infinity isn't part of first-order Peano arithmetic.)
Nov
17
awarded  Critic
Nov
17
awarded  Supporter
Nov
17
comment Can infinity shorten proofs a lot?
You can get the inequality quite easily I think. The log of n! is the sum of log m from 1 to n, which is at least the integral from 1 to n of log x, which is nlogn-n. Done.