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 Sep24 awarded Autobiographer Jul18 comment Explaining Infinite Sets and The Fault in Our Stars Thank you - that simple example fixed the concept for me. I can see that any number x maps to a value in the other set with just a couple of concrete examples. I am not an English major but I suspect this simple example is easily accessible by most folks. Jul18 comment Explaining Infinite Sets and The Fault in Our Stars While I knew the 'point is not a line' was the logical argument against my 'extreme' example, telling someone that the line of (two) points infinitesimally close to the vertex has the same number of points as one infinitely far away from that vertex still stretches credulity in my mind. I am not well versed in set theory so take my comments in that context. I saw this question and just wanted to learn more - and I did by reading a bit in wikipedia about Cantor sets and bijective functions. Although every time I hear Cantor in my mind I am reminded of Eric Cantor. ;) Jul17 comment Explaining Infinite Sets and The Fault in Our Stars @Lucian, Perfect, yes, thank you - think outside the box as it were. But it raises another question in my mind. If we are using this triangle to show that any two line segments have the same number of points, if taken to the extreme then the single point at the vertex would have the same number of points as the longest line segment :/ I do grasp the concept of Cantor's diagonal argument though, where an infinite set does not contain all of the numbers. I believe though, that infinity is simply a useful 'construct' and we should just stop talking about it as though it is an actual number. Jul16 comment Explaining Infinite Sets and The Fault in Our Stars How does one form a triangle when uniting the end points of two parallel lines? Doesn't a triangle have 3 points and don't two parallel lines have four points? Jul14 comment Interview riddle To me, it would seem a better way to ask this question is to posit some function f(x,y) = z given the following examples ... determine the function. I don't see the point in using the standard multiplication symbol when determining how a candidate solves mathematical problems. Jun13 comment 'Obvious' theorems that are actually false I still don't understand how this statement is false. Since 'infinity' does not exist and is only a mathematical construct to aid our understanding of nature it seems to me that anything finite is indeed finite. Mar28 comment What comes after tetration ? And after ? And after ? etc. I've never heard of tetration before so this may be an ignorant question. If exponentiation is 2^2, isn't 2 tetration 2 = 2^(2^2) = 2^4 = 16? And 2 pentation 2 = 2^(2^(2^2)) = 2^(2^4) = 2^16 = 65,536? Jan10 awarded Yearling Dec19 revised Monty hall problem extended. added 9 characters in body Dec19 awarded Editor Dec19 revised Monty hall problem extended. added 47 characters in body Dec19 answered Monty hall problem extended. May3 comment A “simple” 3rd grade problem…or is it? I'm assuming it was down voted because it said the student was wrong then they weren't. Mar28 answered All natural numbers are equal. Mar19 awarded Supporter Jan16 awarded Nice Answer Jan10 awarded Teacher Jan10 answered How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards?