Poll: Does 0.99 Recurring = 1

Duff-Man · 1 Nov 2004 at 17:23

Originally posted by VDO
Ah, but how often do you encounter planks of wood 0.9rm in length in 'real life'? Or journeys oif infinite distance?

In 'real life', you don't have to deal with these concepts, which is, I suspect, why people have so much trouble with them.

Yep.

Many ancient cultures had trouble understanding mathematical concepts which we take for granted, simply because they were always equating numbers to physical objects.

Negative numbers, for example, caused many great cultures problems. After all, what does a sphere of volume -3 look like?!

Rational numbers ('fractions'), irrational numbers, zero, complex numbers - all have had their teething problems involving intuition before they were rigorously defined.

Shadez · 1 Nov 2004 at 17:23

Originally posted by Grrrrr
You mean equal to 0

There is no gap for the reason that has been said several times before: The recurring 9s are NEVER ENDING

so by that logic if there is a gap it has to be NEVER ENDING

(0.1 * 10^-infinity)

if there is a gap then 0.9r cannot be exactly equal to 1......

gambitt · 1 Nov 2004 at 17:28

Originally posted by Shadez
so by that logic if there is a gap it has to be NEVER ENDING

(0.1 * 10^-infinity)

if there is a gap then 0.9r cannot be exactly equal to 1......

ok, what is the gap equal to?

0.00000000...1? where dies the 1 go? on the end of the all the zeros right? there are infinitely many zeros, hence there is no end. so where do you put the 1?

VDO · 1 Nov 2004 at 17:32

Originally posted by Shadez
so by that logic if there is a gap it has to be NEVER ENDING

(0.1 * 10^-infinity)

if there is a gap then 0.9r cannot be exactly equal to 1......

0.1*(10^(-infinity)) is what they call "0.0r1", am I correct? Then see:

Originally posted by AlphaNumeric
Is 0.0r1 the closest number to zero you can get?

What about (0.0r1 + 0)/2 ? The average of 0.0r1 and 0. Obviously thats between 0.0r1 and 0, but 0.0r1 is the closest to zero possible.

(0.0r1+0)/2 = 0.0r1

0.0r1 = 2*0.0r1
Take 0.0r1 from both sides
0.0r1 = 0

Satisfied? If 0.0r1 isn't the closest number to zero, what is? After all how can you get smaller than infinite zeros and then a 1?

Now, if there's nothing between "0.0r1" and zero, that means...?

daz · 1 Nov 2004 at 17:34

Originally posted by Shadez

if there is a gap then 0.9r cannot be exactly equal to 1......

There is no gap - only the gap between your ears!

Shadez · 1 Nov 2004 at 17:35

Originally posted by gambitt
ok, what is the gap equal to?

0.00000000...1? where dies the 1 go? on the end of the all the zeros right? there are infinitely many zeros, hence there is no end. so where do you put the 1?

Ahhhh, but you could also say when do you stop adding 9's to 0.9r? there are so many 9's where do you stop?

Fusion · 1 Nov 2004 at 17:37

Originally posted by Shadez
Ahhhh, but you could also say when do you stop adding 9's to 0.9r? there are so many 9's where do you stop?

You don't. And you don't add them, there are an infinite number already.

VDO · 1 Nov 2004 at 17:38

Originally posted by Shadez
Ahhhh, but you could also say when do you stop adding 9's to 0.9r? there are so many 9's where do you stop?

You don't stop. You don't stop because you don't add nines in the first place.

You're not bloody well typing it into a calculator, it's a number in its own right, consisting of an infinite number of 9's. That's how it is *defined*. Adding anything changes the value! Again, stop thinking in terms of 'real-world' applications!

gambitt · 1 Nov 2004 at 17:38

Originally posted by Shadez
Ahhhh, but you could also say when do you stop adding 9's to 0.9r? there are so many 9's where do you stop?

but you're missing the point, you don't stop! the 9's go on forever, there is no 'end' so you cannot add another 9 on the 'end' of 0.9r.

a circle is infinite. agree? ok, now draw a complete circle and tell me where the end is.

Shadez · 1 Nov 2004 at 17:39

Originally posted by VDO
0.1*(10^(-infinity)) is what they call "0.0r1", am I correct? Then see:

Now, if there's nothing between "0.0r1" and zero, that means...?

That means you havent understode what i have been trying to say. Or ive not explained my self properly.

VDO · 1 Nov 2004 at 17:41

Originally posted by Shadez
That means you havent understode what i have been trying to say. Or ive not explained my self properly.

So exactly what are you trying to say, then?

Is 0.1 * 10^-infinity not the same as 1/infinity?

Shadez · 1 Nov 2004 at 17:42

Originally posted by gambitt
but you're missing the point, you don't stop! the 9's go on forever, there is no 'end' so you cannot add another 9 on the 'end' of 0.9r.

a circle is infinite. agree? ok, now draw a complete circle and tell me where the end is.

oh dear, maybe i should have put a

at the end of that comment.

Shadez · 1 Nov 2004 at 17:54

Originally posted by VDO
So exactly what are you trying to say, then?

Is 0.1 * 10^-infinity not the same as 1/infinity?

Im tring to say that both sides of the argument are correct.

0.9r = 1 beacuse the differece is so infinatly small that it cant be measured, but this does not mean there is not a difference between 0.9r and 1 just that it cannot be quatified.

there for i say

0.9r != 1

0.9r = 1

Fuzor · 1 Nov 2004 at 17:55

to all common purposes it does = 1

gambitt · 1 Nov 2004 at 17:56

Originally posted by Shadez
Im tring to say that both sides of the argument are correct.

0.9r = 1 beacuse the differece is so infinatly small that it cant be measured, but this does not mean there is not a difference between 0.9r and 1 just that it cannot be quatified.

there for i say

0.9r != 1

0.9r= 1

but you can't actually tell us what the difference is can you? I mean, not even in notation form... and no 0.0r1 is not possible, because you can't say x = infinity + 1

Shadez · 1 Nov 2004 at 17:58

Originally posted by gambitt
but you can't actually tell us what the difference is can you? I mean, not even in notation form... and no 0.0r1 is not possible, because you can't say x = infinity + 1

yes i can the difference is,

0.1 * 10^- infinity

Killerkebab · 1 Nov 2004 at 17:58

Now surely you can't put "infinity" in an equation?

gambitt · 1 Nov 2004 at 18:01

Originally posted by Shadez
yes i can the difference is,

0.1 * 10^- infinity

ok

0.1 * 10^-infinity
= 0.1 / 10^infinity
= 0.1 / infinity
= 0

Bodak · 1 Nov 2004 at 18:04

Originally posted by Shadez

0.1 * 10^- infinity

Would people stop putting infinity into an equation like a number? You're making me cry.

Consider
0.1 * 10^-n

Now consider Lim n->inf [0.1 * 10^-n] = 0

Shadez · 1 Nov 2004 at 18:06

Originally posted by gambitt
ok

0.1 * 10^-infinity
= 0.1 / 10^infinity
= 0.1 / infinity
= 0

please give me the value of infinity so i can check your workings........... or prove to me in a iron clad way that a fraction / infinity = 0

Poll: Does 0.99 Recurring = 1

Does 0.99 Recurring = 1

Yes

No