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None of these, except 0.999… and 1 are well-known standard objects in this setting. You have to define what you mean.
by gspr 7y ago
None of these, except 0.999… and 1 are well-known standard objects in this setting. You have to define what you mean.
- brutt 7y agoI defined it: 0.000...1 = 1/10^∞ = 1/∞
- gspr 7y agoThat's not a definition. Neither 10^∞ nor 1/∞ is defined in any standard system, so you'll have to define those too if you want to use them to define 0.000…1.
- brutt 7y agoSee https://en.wikipedia.org/wiki/Surreal_number https://en.wikipedia.org/wiki/Surreal_number .
- gspr 7y agoYou're working with surreal numbers? This is not what people would expect unless it's explicitly stated. In addition, you're likely going to have a hard time explaining surreal numbers to someone who struggles to grasp that 0.999... = 1 in the ordinary reals.
- drran 7y agoSurreal numbers and infinistemal are simpler to work with when you need to work with infinite series. Here John Conway explains them: https://www.youtube.com/watch?v=1eAmxgINXrE https://www.youtube.com/watch?v=1eAmxgINXrE