alt Hacker News> Infinity is a mathematical symbol we can observe.
This is like confusing the map for the territory.
Symbols live in syntax (like the syntax of programming languages), while mathematical concepts live in semantics. Infinity is not a symbol, it's not ∞. ∞ is the symbol we use to represent infinity.
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IsTom • yesterday at 7:10 PM
There is a way to look at mathematics as just a bunch of rewrite rules for things on paper. It might not be particularly inspiring, but it's a valid way to look at things.
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The number 42 is also a mathematical symbol we can observe. (Or two symbols, depending on how you want to define symbol).
You can observe the symbol. You can observe 42 of some object, 42 sheep for example.
You can observe a pie chart, or an actual pie, with 42% of it missing.
You can observe a plank of wood that is 42 inches or centimeters long.
But you can't observe 42 itself.
It is not like a hill on a map, where there is a symbol, and there's an actual hill.
It is an adjective and not a noun. It's not real unless it is describing something else.
My point being that regular finite numbers are not real either. So what's wrong with infinity? Or the square root of 2, or pi?