It is tempting, soothing even, to think of mathematics as a perfect edifice of logic and order. The truth, however, is that it is an art as well as a science, and it has places where absolutism breaks down.
For this example, we will show that 0 = 1. First, however, I should point out that when adding a series of numbers, the associative law says that you may bracket the sums as you like without any effect.
1+2+3 = 1+ (2+3) = (1+2) +3.
So, with that established, consider adding an infinite number of zeroes. No matter how much nothing you gather, you will still always have nothing.
0 = 0+0+0+0+0+…
Since 1-1 = 0, you can replace each zero in your sum, like so:
0 = (1-1)+(1-1)+(1-1)+(1-1)+(1-1)+…
From…
