/sci/ - Science & Math

>>11575455

There are maybe 10 or 50 irrational numbers that a computer could be taught to deal with to some limited extent, but the vast majority of them are uncomputable.

But that is besides the point. Watch the numberphile video. He directly says that the Real set was invented as a method of ignoring infinitesimals.

===============
So imagine you have this idea for 1/2, but I "prove" that 1/2 can't exist by invoking the rules of Whole numbers. And when you try to tell me that you are thinking beyond the Wholes, I simply insist that you aren't because all these other irrelevant activities happen in the Wholes. Does this sound like reasonable behavior?

That is why this .999... discussion can never end. You have trapped yourself in this circle of Real Numbers, and refuse to think outside of it, even though Surreals and Hyperreals are well established concepts in mathematics.

>>9844800

Zeno's paradox starts by defining a finite distance. When the runner runs half way, he isn't defining the distance, that has already been done. He is just measuring it. So it isn't the distance that is infinite, just the measurement or description that is.

I suspect that Zeno used this paradox to see who could really think, and who just wanted to venerate mystery.