In the discrete number system, there are no numbers between 5 and 6, you are correct. However, we aren't talking about the discrete number system. The rule for all real numbers is that if two numbers do not have a number between them, they must be equal.

Unless EvF (or anyone) specifically stated that we were talking about anything other than real numbers, real numbers should be assumed. It's not some amazing "get out" argument to suddenly insist that this doesn't work with discrete numbers, we are well aware of that.

(October 19, 2009 at 2:51 pm)Meatball Wrote: I think it might be better to use 'there exists no number that you can add to .9r such that the result is 1' than 'there exists no number between .9r and 1'

• For every x and y, where x and y are real numbers and x < y, there exists a positive real number, z, such that x + z = y.
• There exists no real number that you can add to .9r such that the result is 1, and vice versa
• Therefore, we can conclude that .9r = 1.

Any of the deniers in this thread, feel free to show me a value of z that breaks this argument. If .9r is so obviously a lesser number than 1, it shouldn't be a big deal, right? So what is it?

For all the beans: 1 - .9r = _____

I like that Meatball. Well put.

The only reason there is no number is because the infinite card is played. What about an infinite series of 0.1... ? In the same way there can be no number between 0.1... and 1 for the same reason.. so every infinite greater than 0 = 1

0.2... = 1
0.3... = 1
0.4... = 1
etc

Wow. Just wow fr0d0.

Ok, let's find the number between 0.1... and 1 shall we?

(0.1... + 1) / 2
1.1... / 2
0.5...

Heck, this is too easy. Let's do them all:

(0.2... + 1) / 2
1.2... / 2
0.6111...

(0.3... + 1) / 2
1.3... / 2
0.666....

(0.4... + 1) / 2
1.4... / 2
0.7222....

So yeah...epic fail on the mathematical front there...

(0.1... + 1) / 2
1.1... / 2
0.5... * 2
1.1... - 1
0.1...

I'm sorry where's the number that adds to 0.1... to make it 1? Remember we're only discussing Meatball's theory now.

(October 19, 2009 at 6:05 pm)fr0d0 Wrote:

(October 19, 2009 at 2:51 pm)Meatball Wrote: I think it might be better to use 'there exists no number that you can add to .9r such that the result is 1' than 'there exists no number between .9r and 1'

• For every x and y, where x and y are real numbers and x < y, there exists a positive real number, z, such that x + z = y.
• There exists no real number that you can add to .9r such that the result is 1, and vice versa
• Therefore, we can conclude that .9r = 1.

Any of the deniers in this thread, feel free to show me a value of z that breaks this argument. If .9r is so obviously a lesser number than 1, it shouldn't be a big deal, right? So what is it?

For all the beans: 1 - .9r = _____

I like that Meatball. Well put.

The only reason there is no number is because the infinite card is played. What about an infinite series of 0.1... ? In the same way there can be no number between 0.1... and 1 for the same reason.. so every infinite greater than 0 = 1

0.2... = 1
0.3... = 1
0.4... = 1
etc

Wow... you don't even get the basics do you?

0.2... is not equal to 1 because 0.22 > 0.2... and 1 > 0.22

0.1... + 0.8... = 0.9...

0.9... is provably 1

Tada!

Haha! /damn.. that works quite well ..all I'm doing here is trying to think about it k?

So VOID...
1 > 0.99 > 0.9...
1 > 0.9... ?

Adrian,

I think Loctite makes a product this thread could use.

http://www.loctiteproducts.com/products/...8&plid=695

I know, it would ruin your fun huh?

Rhizo

(October 19, 2009 at 6:48 pm)fr0d0 Wrote: Haha! /damn.. that works quite well ..all I'm doing here is trying to think about it k?

So VOID...
1 > 0.99 > 0.9...
1 > 0.9... ?

Wait... how did you get 0.99 > 0.9...???

1 = 0.9... > 0.99

theVOID made a slight error in his previous post:

theVOID Wrote:0.2... is not equal to 1 because 0.22 > 0.2... and 1 > 0.22

0.22 is actually less than 0.2... (since 0.22 is 0.2200000000.... and 0.222.... is obviously larger by 0.002222...)

What he should have said is that:

0.2... is not equal to 1 because 0.23 > 0.2... and 1 > 0.23.

Thus 0.99 is less than 0.99... (by 0.0099999...).