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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 Δ*x*. 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 Δ*x* ≠ 0. Then there can be only one good answer

Actually, that's also very logical.