Infinities at Ekko and Abel’s Tower
- @ 02:06–03:10: Introduction: To USA as a visiting scholar at University of California, Berkeley.
- @ 03:10–08:29: The number 0,999... is the same as 1. Limits. Proofs.
- @ 08:29–11:15: The number 0,999... is not the same as 1. Infinitesimals. What are numbers? Models of numbers.
- @ 12:14–13:08: On proofs. A spectrum. Formal verification.
- @ 13:18–13:55: The conclusion on 0,999... Non-standard mathematics.
- @ 31:43–40:12: Why is –1 × –1 equal 1? In mathematics we choose some things, and other things follow. Models for understanding and numbers. The number line. Scaling. Debt and counting carrots.
- @ 40:12–41:35: How to prove it? We can start with the assumption that x = –1 × –1 and prove that x = 1.
- @ 51:50–53:10: About nothing. About understanding through thinking about what the opposite is. Negation.
