Is there a sum of all numbers?
Yes, the sum would be zero...
As for every positive number, there is a negative equivalent, so they cancel themselves when summed leaving only zero...
You can never cancel out zero, it is always there, it is just hidden when looking at +1 in relation to zero...
So if you had the totality of all possible numbers, both negative and positive, the totality would equal zero if the numbers were summed...no matter if you had an infinite number of positive numbers or and infinite number of positive sets of numbers, they would be canceled out by an equal number of negative sets and negative numbers, resulting in zero...
See, numbers themselves, which are just mental concepts having to do with the relationship of material objects have no size, no weight, no mass, no energy...which of course would make then non existent if we measure existence by empiricism...
Numbers exist on the mental field, not the physical field. If we see the numeral 1 on anything, we don't actually see the concept of one we see an agreed upon shape or symbol of something that represents the concept of one, a symbol of the concept of one. The symbols represent something else. Someone who had never see 1 used for the concept of one that we agree upon, would not look at 1 and think one. He might have grown up using 2 as the symbol for the concept of one. If the person had no training in math, the numerical symbol of 1 would have no meaning at all to him.
Math is the universal language, because it is beyond the symbols we use, beyond the differences in language, and because it is true for all people, through all time and space assuming they are educated to understand spatial relationships.
Math was not created, it has always existed. Just try to imagine any situation that would create a condition where the principles of math did not exist.
Impossible...
The same with the concept of totality. There has always been a totality, there is a totality, and there will always be a totality. That totality cannot be increased or reduced by something outside of the totality, because by definition the totality includes everything that exists or could possibly exist.
If you did sum all the positive and negative numbers, you would still have the totality of zero remaining...
However, zero is never empty, because it contains all numbers, both positive and negative in a virtual potential state. Zero is a constant, it is absolute, and it is the origin of everything else, including all numbers. Something is understood by its relation to nothing.
You can negate something by introducing its opposite value, but you can never negate zero because zero has no opposite value. Have you ever seen a -0?
Thus zero is absolute, and the numbers are relative because they exist in relation to other numbers.
The totality of zero and all possible numbers added or subtracted from zero is still zero, so zero remains at all times and is complete, zero is a totality which never changes, and could never change.
Quote from WaveStrider:
The term "Totality" is ill-defined. So, by the way, is "God".
If you start with the equality as conclusion rather then premise, then there is no debate.
However -it is true that the premise of Totality+1 is interesting, and not necessarily illogical. Calculating to the last digit of Pi cannot be expressed in it's totality, as it is infinite. Totality is a measuring description denoting the aggregation of a sum.
Which goes back to how you define "God"...