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I think the mistake in your thinking is that infinity is a value or reachable destination. It's a concept and it behaves differently than a number. Also go rea
by qppo 6y ago
I think the mistake in your thinking is that infinity is a value or reachable destination. It's a concept and it behaves differently than a number.
Also go read Generatingfunctionology and Concrete Mathematics
- ristos 6y agoThat's the point I'm trying to make actually. 1/infinity is an infinite series, which would be a computation that takes infinite time to compute. Saying that 0.9999...=1 is saying that the infinite series is the same as that concrete value, which don't actually know and can't prove.
- qppo 6y agoI think the hiccup here is the notion that an open form expression doesn't have a closed form representation, which is not always the case. Closed forms exist for infinite series and vice versa. 1 - sum{k=1}^{\ifnty} 10^-k is one example.