316 reputation
215
bio website
location
age
visits member for 3 years, 4 months
seen Sep 11 at 15:18

Nov
24
comment Algorithm Analysis on Recurrence Relation.
This question might actually be more appropriate for the cs site.
Nov
18
comment Prove using mathematical induction that for every positive integer n, $\sum_{i=1}^n ( i * 2^i ) = (n-1) 2^{n+1} + 2 $
It's false for $n=1$.
Nov
14
comment Absolute Value Properties
Forgot about the most basic case somehow..
Jul
26
comment “Fixed $k$” in Mathematical Induction
What is the justification for proving a universal statement by means of providing a proof for a single $k$?
Jul
17
comment When do I use “arbitrary” and/or “fixed” in a proof?
Are you confusing arbitrary and fixed with free and bound variables?
Jul
17
comment “Fixed $k$” in Mathematical Induction
@GitGud: Are you saying the same or opposite thing as Qiaochu Yuan math.stackexchange.com/a/46728/11444 ?
Jul
17
comment “Fixed $k$” in Mathematical Induction
I don't understand your answer.
Jul
17
comment “Fixed $k$” in Mathematical Induction
Is that the case? Why does he say "arbitrary but fixed" instead of just "let $k$ be an integer"?
Jun
10
comment Prove Satisfiability of Property by Set
I'd love to chat whenever you're up to it: chat.stackexchange.com/rooms/9178/satisfiability
Jun
9
comment Prove Satisfiability of Property by Set
I thought that was the meaning of my question. :( My question was based on an exercise in Apostol's book. Now I'm not certain my understanding of the terminology is correct. I did not understand "is satisfied by the rational numbers" to mean "is true of the rational numbers"; I understood it to mean "no reals beyond the rationals are needed for the property hold". Please correct me if I'm wrong.
Jun
9
comment Prove Satisfiability of Property by Set
@amWhy: I'm trying to prove that there is no implication from the archimedean property that there are real numbers which are not rational, are we on the same page?
Jun
9
comment Prove Satisfiability of Property by Set
You are proving "For all rational a,x,y, if a≤x<a+y/n for all positive integers n, then a=x." I'm trying to show that there is no implication from the archimedean property that there are real numbers which are not rational.
Jun
7
comment Prove Satisfiability of Property by Set
Given the context I provided, I don't see how, by definition, the rationals satisfy the archimedean property.
Jun
7
comment Prove Satisfiability of Property by Set
Given the context I provided, I don't see how, by definition, the rationals satisfy the archimedean property.
May
27
comment Proof of Real Number Property
Alas, the proof of that statement is the very point of my question.
May
27
comment Proof of Real Number Property
While your answer is helpful, you state "for any x<1 there is an element y∈T such that x<y" without proving it.
May
1
comment Proof for Singularity of Additive Identity
@user6981: I believe I was a bit more generous than that. Besides, Apostol isn't giving a better explanation of that proof; he's giving a different one.
May
1
comment Proof for Singularity of Additive Identity
I know he doesn't say explicitly say this is the only way to prove it, but he does repeatedly emphasize the dependence on the cancellation laws. I just wanted confirmation that I wasn't missing something.
May
1
comment Proof for Singularity of Additive Identity
Strangely, Apostol seems to emphasize that the exclusivity of $0$ depends on the Cancellation Law.
May
1
comment Proof for Singularity of Additive Identity
So is the alternative proof indeed valid?