what is the sum of all real numbers?
2007-07-11 15:56:11 · 6 answers · asked by Jay 4 in Science & Mathematics ➔ Mathematics
note: real numbers include negatives and irrationals and blah blah...
2007-07-11 15:59:53 · update #1
The sum is undefined.
It's not true that the sum is zero. There are infinitely many numbers on both sides of zero, but there are also infinitely many numbers on both sides of any other real number. Zero is no more the "center of the number line" than any other number.
By the same reasoning that gets you the sum to be zero, you could take the sum to be 1 + (0+2) + (-1 + 3) + (-2 + 4) + (-3 + 5).... in essence, you'd be adding infinitely many twos together, and your final sum would be infinite.
2007-07-11 16:04:34 · answer #1 · answered by Bramblyspam 7 · 1⤊ 2⤋
The reals are not countable and therefore do not have a sum.
Another way to look at it is as a series and the series is divergent since it goes off to infinity (in both directions).
2007-07-11 16:03:38 · answer #2 · answered by Anonymous · 1⤊ 1⤋
This is a divergent series.
The answer for that is also the answer in:
â«[from -â to â] x dx.
=â - â, but the answer is left as that, the result is NOT 0.
Infinity minus infinity but the two infinities are not directly related.
Thus the result is divergent.
d:
2007-07-11 15:59:54 · answer #3 · answered by Alam Ko Iyan 7 · 3⤊ 1⤋
0 because you have an equal number of positive and negative real numbers
2007-07-11 15:58:50 · answer #4 · answered by Dan K 1 · 0⤊ 4⤋
0
for every positive there a negative and thus they balance out
-1+1=0
2007-07-11 16:00:12 · answer #5 · answered by Dill 4 · 0⤊ 3⤋
The answer is 0
2007-07-11 15:59:19 · answer #6 · answered by Anonymous · 0⤊ 4⤋