0.99999~ = 1 ?

Indeed. It approaches 1 and is 1 at the limit. No disagreement there. Isn't that what I said? That at the limit the difference between 1 and 0.999R is 0. I am not arguing with your maths here. I am trying to explain why it still feels intuitively wrong.

In my time at EvC there have been some truly head banging conversations. Ones that have gone down in forum folklore as examples of brazen lunacy. One about the center of the surface of a sphere springs to mind. As does one by Buz about a non-bending steel bar in curved space-time.At this point I feel that this one might be on the verge of going down in history as the Straggler says 1 doesn’t equal 1 thread.

Which is exactly why I am not disagreeing with you?

I think you have hit the nail on the head here. And IGIT has to be commended for asking the right question.Even if we think of 0.999R as the infinitie series 9/10 + 9/100 + 9/1000 + 9/10000 + ...... as is the correct way to think of this then I think in our heads we intuitively do the conceptual equivalent of plotting y as the sum of the series and x as the number of terms in the series. In which case y never actually equals 1.But as you say 0.999R isn't the sum of the series as such. It is the asymptotic value.It all makes more sense to me expressed like that anyway.

Well I was convinced of the wrongness of my initial intuitive assertion pretty much straight away. Just looking at what others had written and thinking about it a bit convinced me of that on a rational level. I just didn't like it. It didn't feel right. I pursued the matter to A) Try and explain why I thought intuition and fact were so at odds B) To find a way of reconciling the two in my own head.I think I achieved both (to my own satisfaction anyway) by thinking of this in terms of an infinite series and asymptotes. As per Message 79All of which Mr Jack had been saying to me in so many words anyway. It was just this particular approach/phraseology that made the penny drop in my own intuitive head.