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In mathematics education, I always disliked the way inifinity is shoehorned into the different sets of numbers and treated as "just another number", so that you
by bergoid 9y ago
In mathematics education, I always disliked the way inifinity is shoehorned into the different sets of numbers and treated as "just another number", so that you can write shorthands like: 1/∞=0, instead of the more accurate ∀ε>0, ∃c>0: x>c ⇒ 1/x<ε
Infinity is not a number. It's a limit.
Treating it as a number only confuses real understanding of it.
- jacobolus 9y agoIt makes sense to treat ∞ ≡ 1:0 as a “number” in the context of projective geometry, the Riemann sphere, etc. The quarrel Wildberger has is not with the proportion 1:0, but with the concept of a limit.
- tnzn 9y agoEvery single prof I have had have forbidden my class to write 1/infinity=0...
- leephillips 9y agoIn 1960 Abraham Robinson invented the hyperreal number system, which contains infinitely small and large numbers. They behave as you would expect. The branch of analysis (including calculus) based on the hyperreals is called "nonstandard analysis". So you can develop calculus without the limit concept using this number system.