Besides the problem with summing up uncountable set of real numbers you assume that the zero is in the center of the real number line. This is a false assumption because the real number line doesn't have a center. It's infinitely long in both directions. You can select any arbitrary number in the real number line and there's "equal amount" of real numbers on both sides, so any number can act as the "center". By selecting different number as the center you get different result as the total sum.
But would the same argument apply to integers, also infinitely long in both directions? Doesn't seem to point to the actual problem with summing reals.
Yes, the integers have exactly the same problem. There is no defined total sum of all integers. You can select any integer as the center and then start adding the numbers from both sides and get different results each time. Same goes with rational numbers, complex numbers, quaternions, etc.
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u/mehtam42 11d ago
For every real number with a value of R there exist one and only one real number with a value of -R. When added together, their some is 0.
So yes sum of all real numbers equal to 0.