Oh, it wouldn't, I'm trying to imply that maybe infinitesimal != 0.
Yes this is as far as I know too, but I found some compelling arguments showing that because infinitesimal is so small, that is, if one were to search for it's 'end', they could never find it, thus making it nothing.
Well, I can't find the pages with the proofs anymore. But here's a good reference nonetheless: 0.999... - Wikipedia, the free encyclopedia...
Now, I hope my assuming that saying that 0.(999) = 1 is the same as saying that 0.(000)1 = 0, isn't wrong
True, and in real life calculations, they're not used. To me, this seems to lead to holes in the mathimatical system, though, for example the infamous divide by 0 problem. The idea is too see how infinity and numbers would co-exist in the same mathimatical system. Formal math seems to say they don't/can't.
We know that infinity is bigger than 1, and that infinitesimal is smaller than 1, so, when a difference in relationship to tangible real numbers can be shown, doesn't that prove that they aren't the same thing? On other words: Surely something can't be smaller and bigger than something else at the same time
The problem with this is the assumption that any operation on infinity results in infinity, for example, 0 * infinity, is of course, 0.
Just as we have 1000, and 0.001, we have infinity, that is, 1(00)0, and infinitesimal, that is, 0.(00)1, I purposed 1 as an answer because if 1000 * 0.001 = 1, then why not 1(00)0 * 0.(00)1 = 1?
This breaks the rules, though.