Logic and Infinity: The Errors of Calculus

Steve Patterson

183

You’re just wrong about basically all of this, and you don’t seem to know any mathematics. I’m not going to go argument by argument and tear it to shreds, because that would just take too long. I’m just going to leave a few basic examples.

- Consider the interval (0,1) which does not contain its endpoints. It has no largest point.
- Consider the definition of an infinite sequence: A sequence s_n converges to s if for every positive e, there is a number N, so that for all n>N, |s_n — s|<e. That is to say, the sequence has a limit if you can make tiny bubbles around the limit point, and after a point, no terms escape the bubbles.
- An infinite series is just a sequence of partial sums. It converges when that sequence does as above.
- There are mathematical concepts of infinity — many different ones. The infinity used in calculus is not the same as the infinity used in set theory, and there are different sizes of infinity.

I hope you spend some serious time with proper mathematics, so you can learn. I recommend the text “Introduction to Mathematical Reasoning” by Eccles. Do the exercises too. They’ll really help you learn.