User blog comment:Simplicityaboveall/Simplicity/@comment-1605058-20141223184654

When looking at images you have uploaded to the wiki, I have found two mistakes in it:

1. You say bijection is "defined as a function that maps each point in set X to exact one point in set Y." The correct definition should be that every element in Y is being mapped to by exactly one point in X.

2. You say that "One could then wonder [...] the set would result in a cardinality of $$\aleph_0+1$$ [...] but it is not the case." In fact this is the case - the resulting set has cardinality $$\aleph_0+1$$. The catch is, $$\aleph_0+1=\aleph_0$$.

Of other things, my honest opinion is that you should get into a bit better detail when discussing correspondence with triples - I think it's not at all straightforward to imagine a spiral moving in all three dimensions.