I love how people without an actual mathematical background make these sort of arguments - not because they're wrong but because it helps me check when I make t

I love how people without an actual mathematical background make these sort of arguments - not because they're wrong but because it helps me check when I make those assumptions myself. Multiplying by the square root of 2 is also a fun one since you need limits to show people that real numbers only make sense with the least upper bound theorem and limits and things they expect to work "intuitively" (like division or multiplication) only have approximate meaning when they use the common operations.