Or is it? Say I'm a layman and I decide that in the system of math as I understand it, 0.000... is larger than 0. Yes, if I was going to be completely form with my own system of math I would eventually have to face the problems this introduces and resolve it, but until then I can generally adopt a self contradictory system and continue to live my life unaffected. Much like many people live their whole lives using naive set theory for their understanding of sets.

Then in your system of math 0.999... is also less than 1.

However, basic arithmetic taught to children requires that adding trailing zeros does not change the value of a number. You'll have a hard time doing arithmetic once you change that assumption.

You are correct. This was a rhetorical question to get traderjane to question whether "bigger than 0" really applies here.