...there are just as many points in a unit square as on a unit line? In other words, the square is not "bigger" despite having a nonzero area.

...infinite sets come in different sizes? For example, there are demonstrably more real numbers than integers.

...the recurring decimal 0.999... is equivalent to one. It's not a smidge less than one, it

*is*one. Don't buy it? What would you say is the decimal of 1/3? That's right, 0.333... Now, just as 3 times 3 is 9, 3 times 0.333... is 0.999..., which is one as surely as 3 times 1/3 is one.

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