[SkyBelow]

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.

[brlewis]

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.