Re:0.999...= 1
by aliceryhl on Tuesday April 28, 2020 @02:08PM
(#23009930)
No, you don't have to accept that. In my Analysis 2 course we worked a whole bunch with [0, ∞], i.e. the positive real numbers together with infinity, and we defined 1/∞ = 0 and ∞ * 0 = 0. You lose some of your usual rules of arithmetic, but it gets a lot easier to talk about integrals.
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https://en.wikipedia.org/wiki/Surreal_number
Quote:
There are also representations like
{ 0, 1, 2, 3, … | } = ω
{ 0 | 1, 1/2, 1/4, 1/8, … } = ε
where ω is a transfinite number greater than all integers and ε is an infinitesimal greater than 0 but less than any positive real number. Moreover, the standard arithmetic operations (addition, subtraction, multiplication, and division) can be extended to these non-real numbers in a manner that turns the collection of surreal numbers into an ordered field, so that one can talk about 2ω or ω − 1 and so forth.
I'm not quite sure I understand what you're trying to tell me? The example I mentioned is not about surreal numbers.
I recommend watching this lecture about surreal numbers by John Conway: https://www.youtube.com/watch?v=1eAmxgINXrE .