Recent content by Adonis1

Yes that's right, thanks for the correction.

Concerning #1, you are right. I guess one would have to either assume the ice cream drops from the top step, i.e. 10m, or make an assumption that it drops from a reasonable height at which it is being held, say 1m. Concerning #2, the professor (not the one in the problem, but the one in the...

Perfecto! Muuah (:kiss:). Again thank you this has all been extremely helpful. I feel as if I'm starting to understand. Hopefully I'm not deluded.

Thanks for your explanation. I agree sets seems the best way to go, and if I'm not misreading you, you seem to be pointing to a similar worry as Gopher identified. Anyway, I think you (two) have helped me achieve my goal. I'm very grateful for your patience and help.

This is exactly what I was looking for! Thank you for this very clear explanation. I do have one question regarding this explanation however. This is certainly good enough for my purposes though, and my question is off-topic, i.e. not related to this problem. Anyway, you say that I can proceed...

Good question. I confess it isn't entirely clear what I meant. Talk of properties is confusing. Perhaps I can ask for a little help here. You said earlier: What did you mean? I thought I understood but now I don't think I did, so perhaps I can try and use your definition and see where it leads...

Please have patience with my slow and feeble mind. I'm not trying to give anyone a hard time, just trying to wrap my head around this. Alright, so it seems to me you are right, when we begin our proof, we can make P any property we choose, say for instance ≠. But then using Set theory and...

:) Because we said we were checking for property P. Say our property P is simply reflexivity. Then 0=0, 1=1, 2=2, etc. Maybe I'm missing something else?

Ugh! I'll keep trying to convince myself :) Thanks for your help. It does seem to be though that induction will have to be an axiom we accept and that is not reducible to any other, like the Well-Ordering. Perhaps that's why Peano didn't take the Well-Ordering Principle as primitive but rather...

Ok I don't see how we know this at this point. This is the conclusion we are aiming to prove, so if we assume it as knowledge, aren't we begging the question? Exactly. Right, if S is the empty set, then S doesn't have a least member and it contradicts the Well-Ordering Principle. So in...

Homework Statement Prove Mathematical Induction using the Well-Ordering Principle. Homework Equations None. The Attempt at a Solution Every solution I can think of, and every solution I've seen, at some point along the proof, seems to me to employ the very reasoning that is used...

It just dawned on me what other moves I need to close the gap, and I picked up on a few other errors above. I don't know why I didn't see it before. Thanks for your help.

Thanks for the prompt reply. So, I'm on the right track but there is a gap that I can't solve in this problem. I glanced after many hours at Spivak's solution and it still doesn't satisfy me. He says the equation: \begin{align*} 0 &\lt \lambda^{2} (y_{1}^{2} + y_{2}^{2}) - 2 \lambda (x_{1}...

I'm just getting started with Spivak and math and am confused about the notation here, perhaps someone can clarify it for me. It seems to me this can be read two ways: (a) \begin{align*} 0 &\lt (\lambda y_{1} - x_{1})^{2} + (\lambda y_{2} - x_{2})^{2}) \\ 0 &= \lambda^{2}...