Infinite Power!

Calculus Level 2

Amanda decides to solve this equation: x ∞ = 3. x^\infty = 3. So, since ∞ = ∞ + 1 , \infty = \infty + 1, she rewrites it: x ∞ + 1 = 3 x ⋅ x ∞ = 3. \begin{aligned} x^{\infty+1} &= 3\\ x \cdot x^{\infty} &= 3. \end{aligned} Then she substitutes the original equation back in: x ⋅ 3 = 3 , x \cdot 3 = 3, and finally concludes that x = 1. x = 1. Clearly this isn't the right answer.

Where did she go wrong?

There is no such thing as infinity She didn't. Her argument is sound Beats me She assumed that the initial equation converges

Geoff Pilling by Geoff Pilling , 53, USA

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1 solution

Geoff Pilling
Apr 28, 2017

This is similar to this problem. It is a mistake to assume that expressions involving ∞ \infty converge.

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