[split] 0.999... equals 1

[Violet]

I saw the thread metaphorically explode... and was actually a little intimidated by it growing page after page after yet another page I'm back though . After reading a number of repeated statements (and a couple new ones), it seems the general consensus can be summed up by Evie's statement here:

So there is an endless end of 9s on the end of 0.9, and then you are suggesting there be a gap?? There isn't a gap, there logically can't be - it is endless it goes on forever, you can't put anything on the end of it to make it =1...so it is 1.

My question: where's the room for it to endlessly go on... if there isn't a space in which to do it? There's your gap.

It's endlessness... makes the number nonfinite (aka infinite). The state of something being finite, is that it has limits... By the very definition of .9^... it can never be finite, because it is limitlessly expanding. This means that that the gap between it and one is limitlessly getting smaller... if the number were to ever finally converge: then it wouldn't be infinite. It would be 1, which is finite. But it never converges, because it is forever increasing in size... but every increase is smaller and smaller.

I'll get onto the other things in good time... because I remain unconvinced after reading many of these pages. Anyway, what are your thoughts to the bold?