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seen Mar 11 at 3:56

Jul
17
revised “Fixed $k$” in Mathematical Induction
changed tag
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"?
Jul
17
asked “Fixed $k$” in Mathematical Induction
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
awarded  Informed
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
revised Prove Satisfiability of Property by Set
Clarified background
Jun
7
asked Prove Satisfiability of Property by Set
May
27
accepted Proof of Real Number 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
27
asked Proof of Real Number Property
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.