The real numbers line isn't countable.
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Replying to @IntuitMachine
Yes, there are only integer values. Everything else is a function, not a value.
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Replying to @Plinz @IntuitMachine
The vast majority of “Real”
numbers are not computable. Unlike pi and e, which are computable, most Reals can’t be specified in a finite way. They can’t be chosen or generated algorithmically (hence Axiom of Choice needed).
Check out #DigitalPhysics to go deeper

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Pascal's triangle can indeed generate ALL (positive) real numbers, can't it? (All possible patterns are calculated, eventually (it's an infinite function).)
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This is precisely the point: "eventually" never happens, no matter how long you wait. Infinity can never be reached, and so nothing can be built from infinities.
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Machine learning can go on indefinitely, though. It can keep calculating along with reality, generating deeper fractals at ever more detail. So any number you want to reach, you can calculate.
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What's the last digit of Pi?
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My point was that you can calculate to any level of detail that you like. It doesn't end, because you can always keep going. But it's still calculatable. Pi isn't really "a" number, though. It's a ratio.
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Ratios are numbers, too. Rational numbers are ratios between integers, and they can be fully known. While Pi is the ratio between circumference and diameter of a circle, it is not a rational number. You cannot calculate all of Pi.
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What do you like as a definition of "number"?
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informally, it is a subsequent labeling scheme
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Labeling what?
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whatever you want
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