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**@ 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.

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