Is Infinity Real?

And then there is the Zeno's paradox argument, which purports to show that motion is impossible.We should be skeptical of all such arguments.Is reality infinite? I don't see how we could ever determine that.It is best to think of infinity as a human idealized concept. The way that the infinite works in mathematics seems to be mostly not a problem, though some people have conceptual struggles over, say, the Banach-Tarski paradox.

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Jesus was a liberal hippie

LOL.For those not familiar, "NaN" stands for "Not a Number", and is defined in the IEEE standard for floating point arithmetic.

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Jesus was a liberal hippie

There are still people who argue that the calculus does not solve the problem.The real problem is that we construct abstract models of reality, and do our computations in those abstract models. The mistake is to assume that the model is reality. Zeno's paradox was due to a model that didn't fit well enough. It's a good illustration of why we need empirical evidence, and cannot just go by our theoretical deductions. But it is still based on an abstract model. And whenever the model talks about the infinite, it has gone beyond what has been tested empirically. The laws of logic don't apply to reality. They apply to the human constructs that we use to model and describe reality. The logic can be done correctly, yet reach wrong conclusions, if it is used with respect to a model that does not fit well enough.

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Jesus was a liberal hippie

That's one way of looking at it. The other way is to see it as saying that movement requires infinitely many stages, and we can only carry out a finite number of those. We don't apply logic to reality. We apply it to our sentences that we use to describe reality. Our descriptions are generally imperfect and incomplete.

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Jesus was a liberal hippie