The infinity experiment

If I say let infinity be 1 (the whole or everything) and every number occurs between 1 and 0 (nothing), how do I represent the actual 1. Then what happens to arithmetic and what happens to infinity the concept?

What is we used a transformation?

T(x)=1/(1+x)

T(0)=0

T(1)=1/2

T(∞)=1

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Flow of words

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