tag:blogger.com,1999:blog-5204863782883637837.post4317510320570482257..comments2024-03-27T20:51:11.303-04:00Comments on Accepting Ignorance: Infinity is a Set, Not a Number.Alrenoushttp://www.blogger.com/profile/11119846531341190283noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5204863782883637837.post-15538438579960358332021-06-16T23:26:54.311-04:002021-06-16T23:26:54.311-04:00For every integer n, there is exactly one even num...<i>For every integer n, there is exactly one even number 2n, so ∞/2 = ∞</i><br /><br />∞/2 = ∞? Divide by ∞, 1/2 = 1. Nope. You can't divide by 0, and you can't divide by [∞]. <br /><br /><i>What is ∞/∞?<br />It could be anything, even infinity!</i><br />Only if ∞ != ∞. This is an error known as equivocation. Maybe ask about Ω/∞ or something, because it's not surprising that 1 != 2. <br />Mathematicians have been extremely dumb about 0 and ∞ for centuries. You can't divide by [∞], and in exactly the same way 0/0 is undefined. <br /><br />What is 2 divided by [6, 4, 7, 333, 0.0009]? Not each individually - all at the same time. In other words, in what way 1/3=1/2? Infinity is a set, not a particular member of the set. <br /><br />Fun fact: 0 does not behave like a number. You can figure it out for yourself. Maybe I'll explain later. Alrenoushttps://www.blogger.com/profile/11119846531341190283noreply@blogger.comtag:blogger.com,1999:blog-5204863782883637837.post-55159883041225638002021-06-16T19:34:47.448-04:002021-06-16T19:34:47.448-04:00What is ∞/2? For every integer n, there is exactly...What is ∞/2? For every integer n, there is exactly one even number 2n, so ∞/2 = ∞. What is ∞/∞?<br />It could be anything, even infinity! There are ∞ × ∞ complex integers, but the complex integers can be serialized by spiraling out from the origin, so ∞ × ∞ = ∞.<br /><br />Infinity behaves in so many ways unbecoming of a number that no sane person would ever call it a number. OTOH, zero meets all conditions of being a number except that you can't divide by it.<br /><br />I think it's safe to say that any finite number divided by infinity is zero. The one thing you can't do with zero is the only thing you can do with infinity.Davenoreply@blogger.com