I love pictures that literally speak 1000 words. Since most of the morons on this site don't understand English, I thought it might be useful to draw some pictures.
In the following JPEG, our delusional mathematician Cantor discovers equal infinities.
The red, orange and blue lines in the following jpeg, have length.
Written as intervals:
and none of the lengths are equal.
Cantor tells us that all these intervals (sets) are equipollent in terms of cardinality.
Eureka! I have discovered equal infinities! - Georg Cantoredes.
I realize that a lot of you are extremely dim, so I'll provide a guide in the form of questions for you:
1. Do you think that the "number of points" is a meaningful idea in any non-finite context?
2. The points correspond to magnitudes. Can we say that the longer lines contain more magnitudes that can be measured?
3. Do all the points actually have a one-to-one correspondence from one line to the others?
4. Cardinality of finite sets is well defined. Can infinity be a cardinal number?
5. Since we can say nothing about infinite sets, it follows that we can deduce much regarding the cardinality of the infinite sets. This is sophistry. True or False?
Assess your level of intelligence:
0 correct answers: Dunce (or Cantor!)
1 correct answer: Moron
2 correct answers: Primate
3 correct answers: Average
4 correct answers: Promising
5 correct answers: John Gabriel is impressed!
Keep an eye open for the next exciting lesson on Cantor's delusions!