Arithmetical Rule That Would Make Infinity Impossible And Argument Defending It

Rule: Every number that is added to a sum must be subtracted from some other sum.
Argument in defence of this rule:
In real life, whenever you add something to a quantity the thing which you add has to come from somewhere else; it has to be subtracted from some other sum.
In real life you couldn't have a sum like 2+ 2 = 4 because that would be like 2 popping into existence from nowhere.
In real life the 2 that you add has to be taken from some other sum.
A more realistic sum would be  6 - 2 = 4 and 2 + 2 = 4.
Now where the 2 that you added came from has been accounted for.
And, if that rule was followed then infinity wouldn't be possible. The only way you could infinitely add 1 to a sum, if you followed this rule, would be to infinitely subtract it from another sum and this is logically impossible.
Why?
Because if you continuously take away 1 from a number, however large the starting number is, eventually you must reach 1.
In other words, infinite subtraction is impossible and, because you need to subtract from one sum to add to another, thus infinite addition would also be impossible.