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We've defined the series we're talking about, and we've defined 0.99... as the limit of that series. I don't know whether repeating decimals are useful for tes
by tom-thistime 6y ago
We've defined the series we're talking about, and we've defined 0.99... as the limit of that series.
I don't know whether repeating decimals are useful for testing equality of surreal numbers.
All I'm trying to say is we're all talking about anything and everything except the definition "when are two real numbers equal?"
And then we're saying people who don't understand the consequences of that definition are kind of dummies ... while we continue to not actually say what the definition is.
- ramshorns 6y agoFair. Maybe the definition is that two real numbers are equal iff there is no real number between them. Which is nonintuitive if you're used to things like natural numbers which have successors. But if you teach people this way of thinking about the real numbers, then arguments like "it's the last number riiight before 1" stop working.