0.99999~ = 1 ?

You appear to be doing in the very post to which I am replying, because you are still questioning the identity of 0.9999... and 1.Those two are different names for the same number. They are identical, because they both refer to the same identity (the same number). The names (the ascii representations) are different, but the numbers referred to are identical (meaning that they are the same number).

Mathematics doesn't work if you talk about it that way. For then we cannot say things such as x = y, because as strings x and y have different shapes.

In mathematics, "equal" means "identical".

The Wikipedia entry on mathematical equality agrees with me and disagrees with you.Incidentally, I do have a Ph.D. in mathematics.

For those confused by Rrhain's diversion, here is the first line of the cited Wikipedia entry.

quote:

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Equality, or more formally the identity relation, is the binary relation on a set X defined by .

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For those who understand the notation, it is quite explicit. Roughly, it says that "x is equal to x, no matter what you take x to be in the domain of interest (numbers, for example). Moreover, that gives all possible cases of equality in the domain of interest. And there, Rrhain begins a big diversion.Sure, the word "identity" has many meanings. In this case, context requires that it be the identity relation (because it is defining the equals relation). And the identity relation is just that things are identical to themselves and to nothing else.If you don't like Wikipedia, then try a google search for equal in mathematics. Or ask your local research mathematician. And expect there to be some disagreement - you never get 100% agreement on anything.

Sorry, but that is gibberish. There is no number named "infinity" and there is no meaning for "infinity - infinity". I am guessing that you misremembered something, for that sure does look garbled. That's a definition of congruence. I'm not sure why you would think that says anything about "equal". It sure seems a reach.The remainder of your post does not even seem to be related to anything else in this thread. And we have drifted far from the topic of the OP. So I'll end my participation in the "equal" side issue.