/sci/ - Science & Math

>>12073969
>>12073986
>>12074042
A line segment is a line with two endpoints. A ray is a line with an endpoint and an interior point. An interval (a,b) doesn't have any endpoints.

>>12073887
Real numbers were rigorously defined by Euclid long before Riemann was born. Your suggestion that Riemann's standard of rigor was "unacceptable by today standards" is completely stupid. I think the thing you're getting at, and failing to get to, is that people started to look for an algebraic definition of R separate from Euclid's perfectly rigorous geometric definition. To people who wanted to overturn thousands of years of tradition in which the reals were fundamentally geometric, Euclid's definition was unacceptable. That has nothing it all to do with Euclid lacking rigor. It has everything to do with their inability to synthesize an algebraic definition with Euclid's definition. They failed to find this synthesis, but I have found it.