If it can't be represented in the physical world does it really exist? [eg]

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My post in emanuela's aformentioned thread:

"Infinity" was once *disproved to me by this explaination:

Take your thumb and your forefinger and spread them apart as far as possible. This represents a distance. Now make that distance one half as large. Continue to cut the distance between them in half.

Theoretically, your thumb and forefinger will never actually® touch each other.

Does my thumb and forefinger ever touch as I understand touch? Or is my perception not only not real but not representable by mathematics (as could be the only proof of touch *contextually)?

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Isn't the infinity of integers 2x that the infinity of only odd integers? If not, then why bother with proving infinity?