[kutkloon7]

Or define what = means. In fact, most university courses make this same mistake.

[umanwizard]

Yeah, this is an abuse of notation (it should be written as set membership, not equality), but the "=" in "0.99... = 1" is really equality, so I don't think this is a good example when talking about that.

[kutkloon7]

True. My point is that equality is never defined well.

[umanwizard]

Never? Equality always means the same thing in every case I can think of, except big-O notation. You picked the one example I'm aware of in all of mathematics where it means something different.

[kutkloon7]

I am not arguing that it is ill-defined. I am arguing that no-one takes the effort to rigorously define it.