Try dividing the numbers one through ten into two groups. Then multiply all of the numbers within each group. Is it possible for the sums to be equal? No. Why? One of the groups contains a seven, so the sum will be a multiple of seven. But there's no seven in the other group, so the sum can't be equal. Which makes seven a very lonely number.
I'm doing poos right now
There are an infinite number of numbers between every two numbers
Okay, so we have 1, 0.1, 0.01, 0.001, 0.0001, 0.00001, ... you can repeat this process infinitely
So, I can just divide the groups up so I have an infinite amount on both sides and get
infinity = infinity
checkmate, OP. Shouldn't have specified real numbers or integers
you mean product
>>8739697
Yeah but the numbers from 6 to 10 are bigger, therefore the sum is bigger too. "infinity" is more of a concept, but if you theoretically managed to multiply all the numbers together, the second group would be bigger
>>8739706
I just do the groups like this:
Group 1:
1.1, 2.2, 1.3, 2.4
Group 2:
1.2, 2.1, 1.4, 2.3
Here I have 4 unique numbers in each group, but the sum is the same. I just alternate every time with the last digit. Both sides will end up being the same kind of infinity
>>8739697
what do you get when you multiply every real number?
>>8739713
Do you mean multiplying every real number between 1 and 10?
Even just from 1 to 2 would be infinite, because there are infinitely many reals between 1 and 2. Even between 1 and 1.1 there are infinitely many reals.
There are infinite infinities.