That's roughly similar to how one of my maths teachers introduced the idea that 0.999... = 1. Introduced x = 0.333..., 10x = 3.333..., 10x-x = 9x = 3, x = 1/3,

That's roughly similar to how one of my maths teachers introduced the idea that 0.999... = 1. Introduced x = 0.333..., 10x = 3.333..., 10x-x = 9x = 3, x = 1/3, and then waited. Eventually one of us made the connection what happens if you set x = 0.999... (or equivalently if you times x by 3 - you get x = 0.999... and x = 1).