To Sara.

I'm leaning on the understanding that your view of everything being equally valid is out of wanting to be loving and accepting. If that understanding is wrong let me know. The following is based on that understanding.

There's a philosophy I've grown up with known by the phrase "love the sinner, hate the sin."

The idea is that we can be loving without accepting other people's flaws as OK. Accept them as much as you can, but don't accept a philosophy that is harmful, or a behavior that is wrong.

It gets deeper from there. The idea that you accept others in spite of their flaws, has a benefit because no one is perfect. Everyone has something they can work on, something they can correct, probably even something that is wrong, harmful or somehow unhealthy. Have mercy on others because you also want mercy. Same with forgiveness. Even to say that it takes a true friend to help another out from continuing a bad path, (such as taking away their car keys when a friend is drunk).

You can accept and love others without accepting their wrongs.

The paper proves

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

At this stage sara242 due to your repeated claims that have been refuted repeatedly I think you are either just a troll for fun or you simply don't understand much about the low foundational levels of maths.

The explanation that I gave you before is 100% valid when you treat the set of integers as a separate object that is not a subset of the reals (but which however may be homomorphically mapped into the reals, ie: for each integer there corresponds a real and the arithmetic operations are preserved, eg: 1-maps_to->1.000.., 2->2.000.. etc where 1+1=2 and 1.000+1.000=2.000, 2*2=4 and 2.000*2.000=4.000, etc) . To recap what I said: since an integer cannot ever equal a real the premise to "when a finite number 1 = a non-finite number 0.999.. then maths ends in contradiction"is always false thus this statement (although overall true) does not by itself allow you to claim the conclusion is true.

If however you are of the opinion that the integers should be considered a subset of the reals the argument still fails because by all the methods used to construct real numbers (Cauchy sequence, Dedekind cuts, Tarski axioms, etc) the integer 1 (which is now actually the real 1.000..) is the same number represented by 0.9999...

Note: technically you are free to chose to treat integers as a separate set or as a subset of the reals- at the end of the day your maths will still work. However, personally I'm adamant that you should keep them separate for reasons of philosophy, practicality, efficiency and history.

By-the-way: the number 0.999.. is a finite number but I assume that you mean the representation is not finite or the process to construct it is not finite or the set that it actually is has infinite members.

What the opinion means about all opinons being valid is

in the every day world this means that all
views are valid but so are the opposing
views valid Thus all civil rights views are
valid ie pro gay marriage is valid but so is
the opposing view ie anti-gay marriage is
valid
as Each view contains within it its negation
as all views end in meaninglessness

also

Now with the inconsistency of language
all possible views and their negation are
now possible and equally valid Thus the
philosophies of Kant Hegal Plato
Aristotle etc all philosophies and the
negation/opposite of the philosophies of
Kant Hegal Plato Aristotle etc all
philosophies are now possible and equally
valid

plus

The paper proves

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

If you repeat a given statement a sufficient number of times, then eventually it will become true.

The catch is, that number may be very big so you might not live long enough to repeat the statement that many times!

There will indeed come a time when all views and their opposites will be equally valid - that is, when the oceans boil as the sun turns into a red giant and no humans remain, thus no views either.

Ok sara, it's obvious that you refuse to even try to understand the flaws in your maths. So let's try another approach.

Did you know that back in the 1890's set theory as then defined/used was found to contain an inconsistency known has Russell's paradox (Russell's found it in 1901 but it was discovered earlier by others). This paradox showed that naive set theory was inconsistent, so for those who used it as a base starting point for maths had to accept the 1+1=3 and any and all other other math statements if they applied the classical logic "principle of explosion" (or in fancy latin "ex contradictione sequitur quodlibet").

But guess what- this revelation that maths was inconsistent didn't change the fact the sun rose the day before this contradiction was found, it didn't change the fact that opposite poles of a magnet attract nor the fact that the a native born Englishman will likely be able to speak English while a Japanese person speak Japanese. Indeed, the only "truths" that it did change were those directly concerning or built upon math.

The point is: So what if maths is inconsistent? This only effects the ability for us to do maths sensibly. We still exist and we are still able to get factual answers to questions that don't involve math by physical empirical observation of the world around us. (eg: facts like the sky is blue, I don't like to experience pain or abuse, animals need to eat, etc.) We can even determine real world facts and compare if they much a particular person's opinion.

By-the-way: when the mathematicians/philosophers did find Russell's paradox, instead of claiming all sorts of weird math results like 1+1=3 all they did was change the underlying foundations so that the weirdness went away: ways they did this was by creating a better set theory (eg: ZFC) and another by was by inventing type theory and introducing a system of types. The world didn't end and not every person's opinion was true.