![]() ![]() He explained that while there is no cardinal number greater than infinity, you could talk about ordinal numbers greater than infinity. <- Does that make sense? Do the infinitely large hyperreals have their own infinity beyond which are numbers that are hyperreal even to the hyperreals?Ģ) I remember watching a vsauce episode on youtube where Michael Stevens explained the difference between cardinals and ordinals, which as I understand it is the difference between numbers that represent quantities and numbers that represent orders. But do the hyperreals have their own 0 point? How could they if they are greater than any real number (I realize some hyperreals are smaller than any real number, but for this question I'm only focused on the infinitely large hyperreals)? If 2 x R means twice the distance from 0 the real number as R is from 0 the real number, the you get a number another infinite distance away-sort of like a hyper-hyperreal number. 2 x n is a number twice the distance from 0 as n is from 0. What does 2 x R equal? It's clear what 2 x n means where n is a real number because there is a 0 value for reference-i.e. I'll start with a couple.ġ) Assume that R is a hyperreal number greater than any real number. So it shouldn't be surprising that someone like me would have a ton of questions. It's like talking about numbers greater than infinity. I'm sure you can imagine how counterintuitive this sounds to someone like me who's new to the concept. ![]() What I understand about the hyperreals is that they are numbers larger than any real number or smaller than any real number. I've been getting into the concept of hyperreal numbers lately, and I've got tons of questions. ![]()
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