/sci/ - Science & Math

I'm pretty sure I just proved that infinitesimals are fucking useless homosexual propaganda invented by engineers

We'll call an infinitesimal any number x such that y + x^k = y for all k>0. It's trivial to say that a sum of infinitesimals is zero.

So consider that you have the sum [math]\sum_{k=0}^\infty x^k =1[/math]

[math]1+x+x^2+x^3+x^4+x^5... = 1[/math]

[math]x+x^2+x^3+x^4+x^5... = 0[/math]

[math]x(1+x+x^2+x^3+x^4...) = 0[/math]

[math]1+x+x^2+x^3+x^4... = 0[/math]
It should be obvious that the left hand side is equal to 1; it's the same expression we started with
Therefore we reach the contradiction 1=0
This is what happens if you put infinitesimals in your math. Degeneracy.