if we have an infinite addition sequence like 0 + 1 + 0 + 1 + 0 + 1 + 0 + 1 + 0 + 1 + 0 + 1 + 0 + 1 + 0 + 1 + 0 ...
but then we add an extra 1 in, like 0 + 1 + 0 + 1 + 0 + 1 + 0 + 1 + 1 + 0 + 1 + 0 + 1 + 0 + 1 + 0 + 1 + 0 ...
then there is an extra 1
but then
there's still an equal number of 0s and 1s
cuz you can still match them all up; (0 + 1) + (0 + 1) + (0 + 1) + (0 + 1) + (1 + 0) + (1 + 0) + (1 + 0) + (1 + 0) + (1 + 0) ...
and the sum is still the same, cuz in the end it all equals 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 ...
therefore, 1 = 0
since it adds nothing