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They said x=0.999...

10x=9.999....

9x=9.999....-x

9x=9

x=1

but this is obviously wrong, you can't substract infinity from infinity unless you consider infinity a number and if so then you would get 8.99...1 and not 9. either way 0.999....= 1 is wrong. and is not different than saying (0.999...) +x=1.99...8 you can't add an infine amount of nines to an infinite amount of nines or subtract. if you could then you would consider infinity as a number and in that case the proof is also wrong