# Proof 0 = 1 This is a meme: Start with the assumption: $a=b$ Mulitply each side by $a$ and subtract by $b^2$ $a^2-b^2=ab-b^2$ Factor out the $a-b$ term: $(a-b)(a+b)=(a-b)(b)$ Divide by $(a-b)$ $a+b=b$ Substitute the original assumption: $a=b$ $b+b=b$ Divide by $b$ and subtract 1 from each side: $1=0$ # Proof 0.999 = 1 For the sake of brevity, anytime 0.999 is written, in implies it repeats for infinity. Set the variable: $x=0.999$ Multiply both sides by 10: $10x=9.999$ Subtract $x$ from each side; $9x=9.999 - x$ Replace the $x$ on the right hand side with the definition from above: $9x=9.999 -0.999=9$ Divide each side by 9: $x=1$ Therefore: $0.999=1$ ![[Connect#Connect]]