Mild Shock
2024-10-01 22:29:52 UTC
Holy shit, what would Cantor say?
Q: Dear Marilyn:
Which is the biggest, an infinite line,
an infinite circle, or an infinite plane?
A: Dear Reader:
I'd say an infinite plane. When comparing
only a line and a circle, no matter how
large they grow, the circle would have the
greater number of points. (For example, a
one-mile-wide circular line "straightened
out" would be over three miles long.) If
the circle were "filled in" as well, it
would have an even greater number of points
an its surface. An unbounded plane surface,
however, would have even more because it
could be said to consist of an infinite
number of infinite lines, laid side by side.
However bad it would be to mow along an
infinite sidewalk, it would be worse to
mow the entire lawn it bordered.
https://archive.org/details/paradesaskmarily00mari/page/184/mode/2up
Q: Dear Marilyn:
Which is the biggest, an infinite line,
an infinite circle, or an infinite plane?
A: Dear Reader:
I'd say an infinite plane. When comparing
only a line and a circle, no matter how
large they grow, the circle would have the
greater number of points. (For example, a
one-mile-wide circular line "straightened
out" would be over three miles long.) If
the circle were "filled in" as well, it
would have an even greater number of points
an its surface. An unbounded plane surface,
however, would have even more because it
could be said to consist of an infinite
number of infinite lines, laid side by side.
However bad it would be to mow along an
infinite sidewalk, it would be worse to
mow the entire lawn it bordered.
https://archive.org/details/paradesaskmarily00mari/page/184/mode/2up