>>43
>>(1+-1)=a
>>(-1+1)=b
These are some basic variable identities. The OP set them up, and 18 continued to use them.
>>a=b=1-1=0
>>a+a+a+...=0+0+0+...=b+b+b+...=0
Just to make sure you're following, he's now showing you how any number of each variable always equals zero, because all of the parts equal zero. It's also setting up one of the most important pieces, which is that a and b are equal.
>>"1 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ....
>> = (1 + -1) + (1 + -1) + (1 + -1) + (1 + -1) + ......
>> = 0"
This is what the OP put, which is then proven wrong in the next bit by substituting in the variables.
>>1=1+b+b+b+...=1+0
>>1=a+a+a+...+1=0+1
>>1=1
This is the final part, which proves the OP wrong.
An arbitrarily long series of A and B both equal zero and are equal to each other. Therefore an arbitrarily long series of A preceded by a 1 equals one. Because a series of A is also equal to a series of B, it is NOT true that a series of A plus 1 is equal to a series of B.
What IS true is that a series of A plus 1 is equal to a series of B plus 1, which is represented by placing the missing 1 at the end of the series.
This then completes the 1=1 identity.