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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 this we will eventually arrive at . Can we write
or is that crap? Can we then write this as
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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.