Recent content by Dods

Next semester I'm probably doing these two courses: a Developmental Psychology course with an emphasis on childhood and infancy and a Foundations of Mathematics course (mostly logic and set theory). I'm really excited about these courses, its a shame I can't do more than two... so I...

Ahh, I read "where 1 and 2 are two distinct objects different from a and b" as meaning 1 and 2 are distinct from a and b, not that they are distinct from each other! In that case my proof does indeed collapse. :-p I knew it was something silly like that. :) But when ##1 \neq 2## I think the...

I think I understand - there isn't a unique codomain as a result of the definitions, but rather by definition (of the triple). I got to catch some sleep but this was bugging me on Wikipedia: 'About the same time as Wiener (1914), Felix Hausdorff proposed his definition: (a, b) := \{...

I noticed something - in Fredrik's post that I quoted, he says that according to the definition of a function that we've been using, each function has many codomains, and according to the second definition, each function has one codomain. I'm not sure I understand this. I think I...

Right, I see, so it's just like the ordered pairs we've discussed, extended to ordered n-tuples. Thanks!

I'm pleased - I'm not that comfortable yet with verbose proofs, you don't really do those in high-school I guess :) I have a question about some terminology I've seen, like "pair" and "triple". In several places I've seen the phrases like "the pair ##(G,*)## is a group if..." or in an...

OK, assuming I understood you correctly and I can take the stated definitions as given, I'll start by proving the Peano axiom: There is no n \in \mathbb{N} such that S(n) = 0 Proof - Lets assume there does exist an ##n## in ##\mathbb{N}## such that S(n) = 0. If we recall the definitions...

Great, thanks :) ^ So you mean I can take this information as "given" or is there a part of this you want me to prove? That should keep me busy! These look great, thank you!

Right. So if I wanted the set of numbers 1,2,3...n, I could write it as n+1 \setminus \{0\} seeing as we said n+1 = \{0,1,2,...n\}? Do you have any ideas for either things I could prove, or define using set theory? I like the problems you give me, they're fun :) Thanks a lot micro :)

I've been reviewing some of the material we've covered and I had some miscellaneous questions: First of all, I've seen A \setminus D type sets and while I've understood them from context, how is the "\" operation defined? ----- Second, let's say we want the set of all functions from...

Unfortunately I can't recommend a book because I'm not familiar enough with personality theory/individual differences. However, I know several textbooks combine Personality and Individual differences, and I would recommend you start with one of those books.

You might like a book on Personality theory or Individual Differences (a book that covers both might be ideal). Studying personality will give you an idea of how people form traits and ways of interacting with the world and individual differences will explain how people are different from one...

I'm not a biologist but I'd find any mechanism, that maintains a trait not directly related to improved reproduction at a higher degree than normal, very interesting, regardless of whether the population is isolated or not. Dods.

Thanks! Once I do the courses I need I'll have a look at that book. :)

Thank you for an excellent explanation! Could you say that for any_1 binary operation *, we can define it as ##*:S \times S\rightarrow S##? That is, a function that takes two elements of the same set to another element of that set? _1 I mean as a basic definition - I assume that you'd need...