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Infinitely large times infinitely small

Infinitely large and infinitely small have no fixed value. The outcome of

∞ × ∆x = ∞

Why is this?

 


Investigation

We start with a few simple calculations

 ,      ,    

The fractions are getting smaller. If we continue, we arrive at an infinitely small number that we call here Δx. Can we write

or is that crap? Can we then write this as

or is that also crap? We know that ∞ × 0 = ?, i.e. it can be any value. In addition, we also know that applies Δx ≠ 0. Then there can be only one good answer

Actually, that's also very logical.

 


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