[Dr Ben]

Hi, I am reading a book set theory (Classic Set Theory - For Independent Guided Study, by Derek Goldrei), and I am stuck on the first paragraph, here it is:

"In the original formulations by Leibniz and Newton of the calculus, and in the extension of this work by such as the Bernoulli brothers and Euler, there were deficiencies of which contemporary natural philosophers were well aware. These deficiencies centered around use of the infinite, namely the infinitely large, for instance the '...' in

1/(1 - x) = 1 + x + x^2 + x^3 + ...,

and the infinitely small, i.e. the infinitesimals used to work out the basic derivatives."

When I see that equation, I just think, well if x = 2, then it is effectively saying that -1 = infinity.

Is anyone able to explain to me why this seems confusing to me?

Thanks,

[ben-smith]

(Original post by Dr Ben)
Hi, I am reading a book set theory (Classic Set Theory - For Independent Guided Study, by Derek Goldrei), and I am stuck on the first paragraph, here it is:

"In the original formulations by Leibniz and Newton of the calculus, and in the extension of this work by such as the Bernoulli brothers and Euler, there were deficiencies of which contemporary natural philosophers were well aware. These deficiencies centered around use of the infinite, namely the infinitely large, for instance the '...' in

1/(1 - x) = 1 + x + x^2 + x^3 + ...,

and the infinitely small, i.e. the infinitesimals used to work out the basic derivatives."

When I see that equation, I just think, well if x = 2, then it is effectively saying that -1 = infinity.

Is anyone able to explain to me why this seems confusing to me?

Thanks,

The series on the RHS does not converge to the LHS (or at all) for values of x not in the range -1<x<1.