Define c as the speed of light in a perfect vacuum.
Begin.
Definitions above considered, you cannot have less than x.
Definitions above considered, you cannot have more than y.
How can one make a claim that a number less than x may exist by deny a claim that a number greater than y may exist?
If a number is less than x it would be -y because it is given that all numbers less than x are the negative counterpart of a number of equal magnitude that is greater than x.
If a number is greater than y it would be -x because it is given that all numbers greater than y are the negative counterpart of a number of equal magnitude that is greater than y.
Well, to start, there is no concept (that I’m aware of) of a “full” set. For a nitpick, no number is either less than or greater than a set, although it does stand in relation to the size of (number of elements in) that set.
Maybe I haven’t given this due consideration, but it’s not entirely clear how anything you say follows from your definitions. Could you maybe explain in more detail what exactly you’re trying to say? I’ll take a stab at what I think you’re asking; please feel free to correct me if I missed the point.
If this is an argument about the natural numbers, then the fallacy is assuming that there is a largest natural number. Given the Peano postulates and the definitions of “addition” and “greater than” (as well as the usual set-theoretic definition of numbers), it’s pretty simple to show that there is no largest natural number. Once you define negative numbers (by no means a small feat), it’s possible to show that there is no smallest natural number (this may be simple, but it’s probably not, so I won’t make that claim).
Ho-lee shit. Sorry for the confusion, ultrafilter. This thread wasn’t supposed to be. Hell, the OP wasn’t even finished or organized or constructed. I was jumbling some shit around earlier today and somehow it got posted. I didn’t mean for it to be, I don’t know how it happened.
Sorry again. Could a mod please get rid of this one, too? It doesn’t make any sense.