>>31
That is the problem with mathematics.It has no connections with reality.
This is true, but I think you feel this way for the wrong reason. Math gives us models, which can then be applied to physical situations. Math is not a description of the physical situation itself, it's a framework to measure some quantitative aspect of the situation. Math often isn't connected to reality in the sense that some models don't apply to anything in the 'real world', or don't give us a useful answer.
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. -- Nikola Tesla
This is, again, very true, but you still need math. For example, good luck quantitatively describing the magnetic field without vector calculus. You just always have to make sure that the 'correct' math you're doing actually applies to the given situation.
So, what is "infinity"?
A vague notion of 'something without boundary' that is useful when building some mathematical models (the Calculus), accurately describes properties on things like the real number line, but is hard to visualize in real life.
Why not use ASSOC lits instead? It would be much easier to think about, than some abstract mumbo-jumbo requiring PhD to understand.
Unless you build something on top of an ASSOC list that has the same properties as a set, what you're saying is nonsensical.
If it
does have the same properties, then every time you see the word 'set', just think of your data structure (I personally don't understand why you'd use an assoc-list...). In fact, I would encourage you to bash out some mathematical ideas you don't find grounded in reality in SLIME. If you do that, you should post your code. I'd be interested in seeing it. I think there was actually a book that did this (in Lisp, even) a while back. I don't know if it was any good or not, because I didn't read it, because I tend to regard the 'foundations of mathematics' stuff as quixotic bat-shittery (okay, Google confirms it was
Meta Math! The Quest for Omega).
>>32
This is a tired philosophical argument, but I sort of agree (although I think you're oversimplifying). You can name a 'thing', but not necessarily find a way to represent/create that thing. On the other hand, if you create a process or description that makes something, you've created a 'thing' with the structure you built (although note that the structure is not the 'thing').