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By slope I mean derivative. Is something being infinity the same thing as being undefined?

Is the slope of a vertical line negative infinity or positive infinity?

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1 Answer

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You can only compute derivatives of functions $f:\Bbb R\to\Bbb R$ (at least in this context here). A vertical line is no such function. So one can consider it as undefined. At least as long as you insist in defining "slope" as derivative.

But infinities are not the same as something being undefined. This depends on the context.

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