Proof of the inconsistency of arithmetics

 Part of aconvergent series onMathematics 2+2=4 v - t - e

The proof of the inconsistency of aritmetics is a pseudomathematical proof used by some creationists to prove that 0=1 as a means to prove that something can exist out of nothing. According to believers of this theory it is fundamental to believe in it because it is a proof that a creator exists. The actual inventor of this proof is Luigi Guido Grandi and was developed by him in 1703. [1].

Proof

The proof can be explained in 4 steps:

1. $0=0+0+0+0+ \ldots$
2. $0=(1-1)+(1-1)+(1-1)+(1-1)+ \ldots$
3. $0=1+(-1+1)+(-1+1)+(-1+1)+ \ldots$
4. $0=1 ~ \blacksquare$

Problem of the proof

At step one it is assumed that zero can be written as an infinitely converging row of values. In aritmetics, such a thing is extremely problematic as you can not know the outcome of infinity multiplied by zero at face value.

Extra notes

The series at step 2 has been named as Grandi's series in his honor. Though Niels Henrik Abel [2] would have probably thought of him as a Satan worshipper.

References

1. http://www.csus.edu/indiv/d/dowdenb/misc/god.htm
2. N. H. Abel wrote "The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever" (Gardner 1984, p. 171; Hoffman 1998, p. 218).