Re:Mathematicians Measure Infinities, Find They’re Equal
by gus_massa on Wednesday September 13, 2017 @08:48AM
(#15237739)
I think you are confusing "arbitrary long" with "infinite".
The leading/trailing zeros are confusing. So many digits are confusing. Let's pick an easy model: The "naïve roman numbers" (This is a made up name, not a technical name.)
Let's consider the set that has
I
II
III
IIII
IIIII
IIIIII
...
IIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIII
...
...
i.e. all the strings that have a bunch of "I" characters.
Each element has a finite amount of "I". If you delete one of them you get a shorter string/number.
The set has strings that are as long as you want. If you print them in a 8pt times new roman font, you can pick one of them that will be long enough to wrap around the Earth, one of the is long enough to reach the Moon, ...
This is an infinite set, where each element has a finite amount of "I".
The leading/trailing zeros are confusing. So many digits are confusing. Let's pick an easy model: The "naïve roman numbers" (This is a made up name, not a technical name.)
Let's consider the set that has
I
II
III
IIII
IIIII
IIIIII
...
IIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIII
...
...
i.e. all the strings that have a bunch of "I" characters.
Each element has a finite amount of "I". If you delete one of them you get a shorter string/number.
The set has strings that are as long as you want. If you print them in a 8pt times new roman font, you can pick one of them that will be long enough to wrap around the Earth, one of the is long enough to reach the Moon, ...
This is an infinite set, where each element has a finite amount of "I".