Does .9-repeating equal 1?

[Kuciwalker]

Originally posted by Darius871
Not gonna read this entire thread, but to all the ladeeda high-and-mighty non-libarts majors calling any opponents idiots, I've seen plenty of post-grad mathematicians dispute this unquestioned dogma as well. A few of the same points they bring up can be seen in these two debates, for anyone obsessed enough to read them:

http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

http://polymathematics.typepad.com/polymath/2006/06/the_saga_contin.html

(Not taking a side here myself, just noting that even among actual "experts" there still is considerable debate.)

No, there's not. In math, once something is proved, it's proved. And the proofs of .99... = 1 are so trivially simple that there's no room for trying to find some flaw in them. It follows directly from the fact that the reals are closed under multiplication that there is no smallest positive number and therefore 1 - .99... = 0 and therefore 1 = .99...

[Adalbertus]

Originally posted by Kuciwalker


The two are basically equivalent.

Not if I tentatively use a base unequal 10.



Using the normal axioms of the real numbers, 0.999... = 1. Of course, there are some graduated mathematicians who like to play with things and come up with axiomatic systems where 0.999... != 1 . I would highly doubt that these systems are of any other use than to provide a system with 0.999... != 1 .

[Kuciwalker]

Not if I tentatively use a base unequal 10.

Yes. The exact same proof works in any base system.

[Adalbertus]

No, because the proof works for 0.(base-1)..., which is unequal 0.999... except for the decimal system. In hex, 1 = 0.FFF...

[Kuciwalker]

You're missing the point. The proof is based on the nonexistance of a smallest positive number.

[KrazyHorse]

Originally posted by Darius871
just noting that even among actual "experts" there still is considerable debate.)

No, there isn't.

You ****ing loon.

[Adalbertus]

You were missing my point, which was that there are circumstances in which 0.999... isn't equal to 1. If you think I was missing the point of the thread: I doubt it has one, other than kidding with maths.

[Drogue]

Originally posted by Lawrence of Arabia
Let a = b

a^2 = ab

a^2 +a^2 - 2ab = ab + a^2 - 2ab
2(a^2 - ab) = a^2 - ab

2 = 1

does TWO now equal ONE???

Even I can spot the hole: 2*0 = 0

[Odin]

Originally posted by Impaler[WrG]


I see your a materialist, so am I

Let me rephrase it, matter and energy exist in descrete patterns that can be expressed with math. That math is real in the sense that it acuratly reflects the actualy or possible configurations and laws of our universe. Not all math describes a material part of our universe nor has every law or part of our universe been corralated with mathematics (yet). Math as we use it is a mental abstraction but its not JUST a mental abstraction, it's an abstraction based on empirical observation that have legitimatly discovered some of the most basic laws of logic. Using the simpler laws we have correctly deduced more complex ones and from them made successfull predictions of the material universe.

Ah, gotcha.

[loinburger]

This is a topic that needs to be revisited every year or two.

[-Jrabbit]

Because the answer might change?

[loinburger]

Eventually we might add enough 9's to make the numbers equal.

[KrazyHorse]

This is a topic that needs to be revisited every year or two.

I hate you.

[Jon Miller]

You should have made a new thread.

JM