1 is a finite number it stops
A finite decimal is one that stops, like 0.157
A non-finite decimal like 0.999... does not stop
when a finite number 1 = a non-finite number 0.999.. then maths ends in contradiction

another way
1 is an integer a whole number
0.888... is a non-integer it is not a whole number
0.999... is a non-integer not a whole number
when a integer 1 =a non-integer 0.999... maths ends in contradiction

This is the concept of convergent series/ sequences I guess.
I guess it can seem like a contradiction- even mathematicians don't know everything about maths- I don't have a good answer for you. I suggest you read more widely. If you can prove something you could win a substantial maths prize. Good luck Sara242.

Sara242 - Are you sure your name isn't Toni Lavis? :)

>0.999... is non finite it cannot be counted-it has no end
Wrong! Being non countable does not something from being finite.

An infinite series producing a finite sum is quite common in mathematics. I suggest you study it, or maybe read a mathematics textbook, rather than making ridiculous claims about a subject you clearly know very little about.

>another way
>fact is 1 is an integer 0.999.. is a non-integer
>when an integer(1) = a non-integer(0.999...)
>we have a contradiction in maths

That's not an actual contradiction; merely an apparent contradiction.
It's evidence that at least one of the following tow assumptions you have made is FALSE:
1) numbers with integer values cease to be integers when they're expressed in other ways
2) integers can't be equal to non integers.

I'm not sufficiently well versed in semantics to tell you with absolute certainty which one you have got wrong, but I think it's the first. AIUI integers are defined by how they can be expressed rather than who they are expressed.

It might help you understand if you expressed your decimals as fractions instead. You're effectively saying that integers are whole numbers not fractions, so 1 can't be an integer because it's equal to 9/9. You're contradicting yourself, but the mathematics remains consistent.

Aiden- I like the series 1+1/2+1/4... = 2

sara42: I'm guessing that you've never studied maths at uni level. If you had then you should be familiar with the various foundations commonly used for mathematics such as Zermelo-Fraenkel set theory ("ZFC"- when containing the axiom of choice) and also should have seen how to construct the real numbers within such a system.

If you study and understand the standard constructions of the real numbers then you will see that your "contradiction" doesn't make any sense. The main problem with it is, is that you are comparing integers and real numbers. But these are completely separately constructed things of maths. However you can embed the integers* into the real numbers in a 1-to-1 fashion. Ie: given any integer and its properties you can produce a unique real number that has corresponding properties. Specifically, when representing reals with infinite decimal expansions, for any integer you can associate a corresponding real which is the same written representation but with an additional infinite number of zeros after the decimal point. eg: the integer 1 maps to the real 1.00000..., 2 -> 2.0000...., -3 -> -3.0000..., also similar for any finite decimal fraction, eg: 0.5 -> 0.500000..., -0.11 -> -0.1100000, etc. See how ALL numbers now have infinite representations and not finite ones.

Also, it is a provable fact that the real number represented by: 0.99999999.. is the same as that represented by 1.00000... . The formal proof is quite advanced for those who've never studied university maths but simple enough that those of average intelligence can grasp it. If you really want to understand it would only take a few months of study. (If you've ever studied calculus at high school you are well on the way because one of the methods used to construct the real numbers does so with a process similar to limits used in calculus- called a "Cauchy sequence": https://en.wikipedia.org/wiki/Construction_of_the_real_numbers and https://en.wikipedia.org/wiki/Cauchy_sequence).

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*: actually, typically you embed the integers into the rationals and then embed the rationals into the reals