Lets Talk About Infinity
Infinity is a number so large we cannot even imagine it. But are all infinities equal?
Lets visualize three sets:
A= 1+2+3+4+5+6+…. i.e. sum of all positive integers
B= 2+ 4+ 6 + 8+ …. i.e. sum of all positive even integers
C= 1+3+5+7+…. i.e. sum of all positive odd integers
All the sums approaches to infinity, but if you look carefully:
A= B+C
Thus A > B
For a long sum B and C will approach each other, i.e B ~= C
So we Can write A ~= 2 B ( Eqn 1)
Thus we can say that not all infinities are equal. The infinity from Set A is greater than infinity from Set B.
But wait,
If you look more closely each number (or object) in Set B is exactly twice of each number in Set A.
So we can write B= 2 A (Eqn 2)
But we had just proved A = 2B from Eqn 1.
So How it is possible.
It Turns out actually all infinities are equal. Infinities are such big number we cannot measure, and physically we cannot assign one Set to be bigger than other unless we measure them first.
Footnote:
Mathematicians Measure Infinities, and Find They're Equal
Image Credit: Mari Carmen Díaz Pixabay