I only ever encountered the limit while learning derivation by first principles in calculus. I understood all the theory behind first principles, but we were never told what happens to the limit h -> 0. Our teacher just said that it goes away after we divide by h, and that’s all I got.
I understand that the limit h -> 0 represents the gap between x and (x + h) getting smaller and smaller. But how does this gap disappear at the end? From searching online I’ve learned that limits are not *equality*, h never *equals* zero, it just gets closer and closer to it. But then why does it equal zero at the end? How is h -> 0 no longer intrinsic to f'(x)? This might be a dumb question but it has stumped me for ages now.
In: 8
It’s mathematicians cheating. We can’t divide by zero so we divide by something really, really close to zero but never *actually* reaching zero. However, at the same time we say it’s so close to zero that we can pretend it is zero compared to the value of x.
Basically we’re having our cake and eating it, making something simultaneously zero and not zero as it suits us.
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