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The general consensus is that his videos are very good. It's just his insistence that the real numbers shouldn't be used that is not accepted. Some mathematicia
by llamaz 10y ago
The general consensus is that his videos are very good. It's just his insistence that the real numbers shouldn't be used that is not accepted. Some mathematicians (1% of 1% of mathematicians) agree with him, most don't.
edit: Doing math without the real numbers is less elegant and harder, but it's philosophically more sound. It essentially means restricting yourself to math that can be described as a (possibly infinite) algorithm.
The lay person is more likely to agree with what Wildberger has to say than a mathematician. In fact, most people think that infinity in math is a process (potential infinity). But in math, we use absolute infinity. A completed infinity. 0.999... does not tend to 1, it _is_ 1. Infinity is completed.
- blux 10y ago> It essentially means restricting yourself to math that can be described as a (possibly infinite) algorithm. I'm confused. My impression is that it is the other way around where irrational numbers and operations like sine, square root etc. are infinite 'algorithms'?
- empath75 10y agoYeah, but there's a difference between saying there exists in reality some exact value for the square root of 2, and saying that it's possible to calculate the square root of 2 to arbitrary precision.