mathematics

Why is 1+2+4+8+… = -1 ?

In a 8 bit CPU register -1 is written as 11111111.

In a 16 bit CPU register -1 is written as 1111111111111111.

And so on.

Say, that our register has an infinite number of bits. Then -1 is written as ….111111.

With the infinite number of 1s on the left.

32 is written as …0000100000.

With the infinite number of 0s on the left.

So we have:

+…000000001 (1 decimal)

+…000000010 (2 decimal)

+…000000100 (4 decimal)

+ ….

+ ….

——————-

+…111111111111 (-1 decimal)

It’s not a joke. At least not more of a joke than the title is.

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5 thoughts on “Why is 1+2+4+8+… = -1 ?

  1. Saladin says:

    The result looks similar than what you get when trying to list the sum of all natural numbers 1+2+3+4+…= -1/12

    Interesting thing, infinity.

    • Both results are from the same line of reasoning. Not everybody is thrilled, thoug. I am quite reserved even toward 1/2+1/4+1/8 … = 1.

      Still, it’s fun to play with hypotheticals, also.

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