Ram, you keep saying things like this, but you never offer anything resembling proof. I presume that's because you consider it self-evident, but it isn't. You need to ask yourself why you believe that - I think the answer is that the two numbers don't look the same, so the back of your mind says that they aren't the same. That's not how mathematics works. There are certain things that must be taken as postulates in order for a mathematical system to get started - once you've postulated those things, though, the rest of the system must flow strictly from logic. If you choose to postulate that .9_ and 1 are, as you put it, "unique" numbers, that is certainly valid. You must be aware, though, that doing so will put you into a system of mathematics which is in disagreement with what the rest of the world has been doing for the past several centuries.ram1024 said:an infinite number of decimal sequential digits of 9 even if it WERE to simply EXIST, it is a unique number and quite simply NOT equal to 1. it is certainly NOT rational whereas 1 is
So, as specifically as you can, without reference to numbers which are not "known" (like the number between .9_ and 1) and without reference to intuition - why are .9_ and 1 two different numbers?