This is known as Galileo's paradox. He started that every number is the square root of something (2 is of 4, 3 is of 9, etc.) but not all numbers are squares. So logically there has to be more numbers than there are squares, but if all numbers are the square root of another number, then there has to be the same number of squares as there are numbers. How is this possible?
2006-08-08 04:24:33 · 10 answers · asked by The1andOnlyMule 2 in Society & Culture ➔ Religion & Spirituality
As locomexican89 posted.
The two sets are infinitely countable. So is the set of rationals.
It might seem strange, but it's true.
And there is no paradox.
2006-08-08 04:36:31 · answer #1 · answered by felix_doc 2 · 1⤊ 1⤋
1 2 3 4 5 6 7 8 9 10....
1 4 9 16 25 36 49 64 81 100...
see how the natural numbers and the squares can be put into a 1-1 correspondence? that means while there are an infinite numbere of each, neither "set" would be greater
2006-08-08 11:32:34 · answer #2 · answered by locomexican89 3 · 0⤊ 0⤋
4 is the square of some number
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
are the square rt of some number.
continue
1000 1001 1002 1003 1004 1005
are the square rt of some number
Continue
1,999,800 1,999,801 1,999,802 1,999,803
are the square rt of some number
continue
1,100,000,000,000,000 1,100,000,000,000,001
are the square rt of some number
go ahead continue
you will find you will never run out of numbers, you may run out of atoms to mark the numbers on
2006-08-08 12:15:18 · answer #3 · answered by Grandreal 6 · 0⤊ 0⤋
Math and religion make for some interesting interplays, but this question does belong in mathematics.
That said, the set of all numbers is infinite, as is the set of all squares of numbers. While the set of all squares is a subset of all numbers, both have infinity as their intrinsic size, so they are technically of the same size, though not congruent.
Many thanks for jumpstarting my brain this morning.
2006-08-08 11:35:16 · answer #4 · answered by Babs 4 · 0⤊ 0⤋
think about it again. eg . what is the square root of 3?.......its
1.7320508075688772935274463415059 right?. and it doesnt end there, it goes on and on....to infinity. therefore there is a slight problem with that paradox
and if this is the way u see it, i hope u'r doubt would be cleared
2006-08-08 11:40:11 · answer #5 · answered by JJ 2 · 0⤊ 0⤋
Both squares and numbers are infinite.
2006-08-08 11:59:19 · answer #6 · answered by Red-dog-luke 4 · 0⤊ 0⤋
There are an infinite number of each. There are not "more" of either. There is no paradox.
2006-08-08 11:27:40 · answer #7 · answered by Anonymous · 0⤊ 0⤋
This belongs in the mathematics section.
2006-08-08 11:27:12 · answer #8 · answered by ChooseRealityPLEASE 6 · 0⤊ 0⤋
well thats how jeebus done do it now you can accept it or be some sill athiest guy or even one of those wandering buddhist guys with thier big great gallon smile
2006-08-08 11:29:33 · answer #9 · answered by the holy divine one 3 · 0⤊ 0⤋
why in religion section?
2006-08-08 11:28:39 · answer #10 · answered by manas hemrajani 2 · 0⤊ 0⤋