If you ignore exponentially small terms they can come back to bite you.
How a question about rainbows led to an entire field of mathematics.
What is 1-1+1-1+1-1+...? How infinite sums challenge our notion of arithmetic.
Usain Bolt, the "fastest man on the planet", aims to get his 100 metre world record of 9.58 seconds down to 9.40 seconds. What has mathematics got to say about this quest?