Thread: Make-a-'dox

Originally Posted by arby

now can you figure out whats wrong with the 0.99999999999 repeated = 1? =P
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There's nothing wrong, that statement is true. (lets just hope I can get the fractions to work)
You start with 1 and divide it by 3 yes? You get 1/3 or 3/9 or 0.333333333 recurring
What is 3/9 divided by 3? 1/9. ( because 1/9 multiplied by 3 = 3/9 )
What is 0.333333333 divided by 3? 0.111111111 recurring yes?

so:
1/9 = 0.111111111 recurring. Double this and get:
2/9 = 0.222222222 recurring.
3/9 = 0.333333333 recurring
4/9 = 0.444444444 recurring
5/9 = 0.555555555 recurring
6/9 = 0.666666666 recurring (2/3)
....
9/9 = 0.999999999 recurring
Any fraction where numerator = denominator is 1. 9/9 = 1 = 0.999999999 recurring (but only if it carries on forever, if it ends then its just really really close to 1)

No need to round, fractions and absolute values proves it. Hurrah.

Oh and the other series of equations, when you divide by (a-b), you are dividing by (a-a), you are dividing by zero. Dividing by zero does really funny things, like produce infinity and ruin perfectly good graphs (like y=1/x, y=tan x and so on)

Edit: MSG already spotted the divide by zero buisness. Sorry

Originally Posted by lord_cliff_turtle

You start with 1 and divide it by 3 yes? You get 1/3 or 3/9 or 0.333333333 recurring
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No. you. don't.

0.3~ is a precise number. We're talking about 0.9~ here, not about 1/3+2/3.

One third is a fraction of one whole. Whilst fractions like 0.3~ are just that - themselves. When writing 0.3~ we're not talking about one third (1/3) of one whole, we're talking about zero-point-three-recurring - that precise number.

That is why the above explanation isn't valid. You're trying to prove what a precise given number is (0.9~ in this case) by turning it into a fraction of one whole. That has no place.

0.9~ is a fraction with an endless period that will never reach 1. It just is by definition of what an endless period is and thus it isn't 1 now and it will never be 1, so to speak.

1/3+1/3+1/3 does equal to 1
0.9~ is a different value than 1 - an eternal value that is never a precise one without rounding but nonetheless.

Awwwww, and I thought I was making sense. I blame my maths teacher who explained it to me in the first place 3 years ago. I understood it then and thought that 0.3 recurring was the same as 1/3.
Can I try another explanation by you (also from the same teacher)?

say x=0.1 recurring
then 10x = 1.1 recurring
if you do 10x - x, you get 9x, which due to recurring numbers after the decimal point cancelling, = 1
(the .1111111.... cancels with the never ending 1.1111111.... of the other due to the nature of recurrence)
thus, 9x = 1
since x=0.1 recurring, 9*0.1 recurring = 0.9 recurring.
these two statements of "9x=1" and "9x=0.9 recurring" appear to prove the equivelance(spelt right?) of the two numbers

Not sure how we can decide which is right though, need to ask for second and third opinions. I shall ask my Advanced Higher Maths teacher tomorrow.

Sorry if I irritated you Merlock

the fault lies within trying to multiply a irrational, recurring number by 10. What happens is, you move the decimal point over to the right. Normally this would mean there are now fewer numbers on the right.

9.99 x 10 = 99.9

But, with an infinately rucurring number, people simply "add" another nine at the end. Technically it should reccur infinatly minus one.

So, then technically, you aren't multiplying by 10 but rather simply adding nine. Then, you subtract the original number. Lo and behold, you're left with nine. Go figure.

Originally Posted by lord_cliff_turtle

say x=0.1 recurring
then 10x = 1.1 recurring
if you do 10x - x, you get 9x, which due to recurring numbers after the decimal point cancelling, = 1
(the .1111111.... cancels with the never ending 1.1111111.... of the other due to the nature of recurrence)
thus, 9x = 1
since x=0.1 recurring, 9*0.1 recurring = 0.9 recurring.
these two statements of "9x=1" and "9x=0.9 recurring" appear to prove the equivelance(spelt right?) of the two numbers
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Sorry, your third step is faulty. Nothing cancels anything out. 10x - x with x=0.111~ would be just that - 9.111~
Bringing a variable into this is needless since the value is a given. Whatever that result above is, is merely a misconception due to the use of that "x". Since x is a given of 0.111~ then 9x is just 9 x 0.111~, which is 9.111~. No need to get confusing with other manipulations.

But aside from that, this isn't the point. The point is that 0.999~ doesn't need to be proven to be equal to 1. It just isn't by definition of an infinite period. It will never reach 1 and will always remain less than 1, being a fraction with a neverending period. There's just no meaning behind this entire deal concerning 0.999~.

Sorry if I irritated you Merlock
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Hahah, no, I don't get irritated often. It's MSG and Kaniaz that were trying to prove an irritating point in IRC...but that's best left alone. o.o

0.33~ is the same as 1/3. Of course it is. There is no argument there.

So this 0.999~ = 1 business. I'll agree, at first it doesn't seem 'right' at all. That's just your lower primate talking (grunting). Ignore it.

Here's the very simple proof, as I think has been mentioned enough times to flog it to death:

1/3 = 0.333~ (it honestly does, just get over it).
2/3 = 0.666~

You don't need to be Einstein to figure that 2/3 + 1/3 = 3/3 = 1.

0.333~ + 0.666~ = 1.

We are writing the fraction in decimal form. So it doesn't terminate nicely. Hey, it's a quirk of writing such a thing in decimals. How about another proof:

1/3 * 3 = 1, doesn't it?

It's all the same thing. It really, honestly is.

We thus see (I hope) that there's nothing magical and unattainable about limits, and so no barrier to grasping that .999~ = 1.[/b]

Read Cecil Adam's article if you still don't get it. He is a lot better at maths than me.

never catch the snail!
ok so a man is standing 100meters away from a snail
and the are going the same direction
the man moves at 10m/s
the snail moves at .01m/s

once the man gets to where the snail started 10s have gone by in that time the snail has moved .1m
the man once again gets to where the snail was the second time and .01s went by in that time the snail moved .001m

you see the man can never catch up with the snail


unless he is chuck norris and he round house kicks the snail into ready to eat escargot

But DocKnubis, didn't you read the article? He does catch up. OK, so it's Achilles and the Tortoise instead of a snail and a guy, but it's the same mathematical principle...right? RIGHT?

mathmatically he never can catch up.
physicaly he will

Originally Posted by docKnubis

mathmatically he never can catch up.
physicaly he will
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Precisely. This is exactly why 1/3 and 0.333~ are different. 1/3 is that physical concept - a theoretical third of one whole, which can never exist in terms of precise mathematics. 0.333~ just like 0.999~ will never reach one third and one whole, respectively - that's your axiom, not 0.333~ being the same as 1/3.

Once again, you can't try and prove what 0.999~ is by turning it into 1/3+1/3+1/3. Because the concept at hand is not 1/3, it is 0.333~, though even 0.333~ doesn't matter here, only 0.999~ does - an irrational number.

When talking about irrational numbers, there is no room for talking about rational/real numbers.

Heh, sorry for the dispute guys. I consulted my teacher for a detailed discussion and - unfortunately for me - although 1/3 and 0.3 recurring are very much like one another, the act of writing them differently makes them different in a minute but important way.
Although it's fun to imagine 0.9 recurring is 1, they aren't the same. Just incredibly close...

Another 'dox: A frog wants to get home on the other side of the pond and it does so by jumping. First off it tries to jump as far as it can, and jumps 1/2 way. Its pretty tired now and so can only jump 1/2 as far as he had before. Jumping again it makes 1/2 the distance of before( 1/2 of 1/2 of 1/2, or 1/8 of the total distance) making him 1/8 from the other side of the pond, but it can only jump 1/2 of that distance.
Will it ever get home? Poor thing...

Really, 0.999 does equal 1. Don't be such girls blouses. Admit it.

I'm with stupid (Kaniaz).

I dont see how. Its like saying "almost" is "completly", or 59 seconds is a minute

though I do see some logic ...

Originally Posted by Kaniaz

Go back in time and do whatever it was you wanted to do, then you won't have a reason for having gone in the first place. You really don't need to get grandma caught all up in this.
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Lol