Math Is Fun Forum

Defining precise concepts is important, so why don't you write a paper on this subject, a well structured document with your ideas, theorems, proofs and beliefs?

But if you want to label it "Mathematics" it must be consistent with existing axioms, theorems, lemmas, etc. Anyway, I would like to see your theory in a formal way so we can discuss what you say with correctness and logical basis.

You can "reach the unreachable" with Limits from good old friend Calculus, and that's all we need to understand that 0.(9) = 1 or some other anti-common-sense equality. "reach" in the sense of "getting really close to".

0.(9) "doesn't exist on the paper", only on our minds because it is a limit. A limit of something. An infinite sum's limit of very small things like 0.009, 0.000009, 0.0000000000000000000009... and it gets smaller as we add up terms. So you can't write it down with a pen, because there is always another term. In the paper, you never reach 0.(9).

it is true that 0.9 <> 1
and 0.99 <> 1
and 0.999 <> 1
and ...etc

but this way you never, never, ever reach 0.(9) = 0.999999999..(inf. # of 9's)

To build the "numeric amount" 0.(9) you need and infinite sum, Limits are implicit here, because you can only know "what are we getting close to" when adding 0.9+0.09+0.009+(...). When you write 0.9+0.09+0.009+... on a paper you are implicitly summing and infinite number of terms, and limits are involved again, even if you don't notice them.

When we mess around with infinity strange things happen, like 0.(9) = 1, lengths become areas, areas become volumes, mass densities becomes masses.. and we enter the mighty world of infinitesimal calculus ^^

It's natural, we sometimes want to explore things our way and create our rules. But later we understand that our efforts were an attempt to reinvent something that already was well-studied and properly defined.

...and it's beautiful, isn't it? ^^