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There is only one type I know of. What are the different types?
Lots and lots and lots. You can find a ton of great information on it, but I'll leave this historical explanation for you as a primer:
Absolute Infinity
And another short video, because it helps to see different explanations of math:
How infinity works
ok I think its clear he meant storing an infinity amount of information with "gives it near unlimited storage capacity." Its clearly not an infinite splicing of a finite type of thing. It seems to be the more common usage of infinite. Honestly I would argue its really not a different type in that the set is finite but the subdivisions are not and ifinite is only refering to the infinte part so storing a value for every infinte cut takes infinite storeage. He is responding to the idea that all knowledge we have now and all future knowledge could be put into the brain ala mastering skills like kung fu.