Hyperreal numbers – where have you been?
You know that question that goes something like, “When does 0.999999 repeating = 1?”
With hyperreal numbers and the infinitesimals, it **does** with Real Numbers but DOESN’T with the Hyperreals.
It’s like a dimension overlaid just on top of this dimensions where everything the same but in that dimension, you gain an infinity microscope and an infinite telescope, letting you look right at that point where one number becomes another number.
I have more studying to do, but this is _definitely_ something I’ve been looking for.
What’s nice about hyperreals is they’re proven by axiom and work great with the real world… the one we see in front of us, where nothing ever *really* stops, where no system is _really_ closed completely… and it makes sense. [to me, anyway].
If I’m understanding it right, that might mean (if it applies to logic) that FALSE *can* equal TRUE – if there is such a thing as “hyperreal logic” – in the hyperreal dimension if not in the actual dimension we’re in. Maybe it doesn’t exist for logic or maybe it does, I don’t know yet.
But as a “more proper” way of looking at how numbers intersect with reality? It’s fantastic. It gives some tolerances to the system.
http://ift.tt/1uGY2G6
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