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ok, I know this might be a stupid question.......

warcrow

warcrow

Lifer
But arent there an infinite number of numbers between 1 and 2? How do we ever get to 2?

Some buddy's at work and I were talking about this.
 
1 finger, 2 fingers


Originally posted by: eakers
yes but there are a countable many rational numbers between one and two, thats how you can get to two.
Click to expand...


But are there any irrational numbers?
 
counting numbers, and continious numbers are different i think...

counting --> 1,2,3,4,5 items..
continious --> think linear graph hehe


donno oh well...hehe
 
Originally posted by: Gibson486
ok, I know this might be a stupid questions.......
Click to expand...

Do you mean question????

Yes, there are an infinite numbers between and two number.
Click to expand...

Thanks I fixed the spelling error.

BTW, do you mean "Yes, there are an infinite numbers between any two number"?
 
Originally posted by: eakers
yes but there are a countable many rational numbers between one and two, thats how you can get to two.
Click to expand...

edit: an infinitely large countable set 🙂
 
Originally posted by: warcrow
Originally posted by: Gibson486
ok, I know this might be a stupid questions.......
Click to expand...

Do you mean question????

Yes, there are an infinite numbers between and two number.
Click to expand...

Thanks I fixed the spelling error.

BTW, do you mean "Yes, there are an infinite numbers between any two number"?
Click to expand...

<<<<------owned😱
 
Oh, and there are an infinite number of irrational numbers between 1 and 2 also.
 
Yes, there are an infinite number of numbers between 1 and 2.

No, if you tried to count every number between them you would never get to 2. You would never even get to 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

No, you are not required to count every number in order to get to 2. It is OK to incerement by discreet intervals.

 
Originally posted by: warcrow
But arent there an infinite number of numbers between 1 and 2? How do we ever get to 2?

Some buddy's at work and I were talking about this.
Click to expand...

There are as many numbers between one and two as there are decimal places you add...You can add all day and never get to the end. But simply because there is no end, does not mean we can't skip them or simply not mention them.

One, two, three. We don't count One point hexabillion and one, One point hexabillion and two, One point hexabillion and three.
 
Originally posted by: warcrow
So how do we get to two then?
Click to expand...

1,2
1,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2

pick any discreet interval x and continuously add it to 1 until you get to 2.

edit: x must take the form x=1/integer for this to exactly come to 2, otherwise it onlt eventually becomes > 2.

 
by not counting every single point between 1 and 2. As Kyteland said, by counting in increments of 1.
Or, if you wish, you could count by 1/2's. 1, 1 1/2, 2.
or 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2

Or 1, 1.01, 1.02, 1.03, ... , 2
or...

edit: I was busy typing when Kyteland posted again 🙂 He's faster
 
rational numbers = whole fractions 3/4, 7/8, 5739/4069897, etc
natural numbers = counting numbers 1, 2, 3, 4... (to infinity)

there are an infinite number of numbers between 1 and 2 (rational and irrational)
so if you tried to count to each one in getting from 1 to 2 you'd never get there
 
Not proof, but evidence that should make it obvious in the case of rational numbers:
3/2, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8, 10/9, 11/10,... is just one simple sequence that shows an infinite number of terms are possible.
 
just because there is an infinite amount doesn't mean they aren't countable.
rolleye.gif


yes there are zillions of irrational numbers between one and two as well but they aren't countable so im ignoring them! hahaha

you can get infinitely close to two without ever touching it but i mean, it comes down to our favorite question:

does 1.999999999999999... = 2?
 
Originally posted by: DrPizza
Originally posted by: eakers
yes but there are a countable many rational numbers between one and two, thats how you can get to two.
Click to expand...

I don't think there are a countable number of rational numbers... I thought there were an infinite number of rational numbers between 1 and 2
Click to expand...

I'm wrong, Eakers is correct. There is a countable number of rational numbers. That's a term that always screws me up because I never stop to think about it. You can have an infinitely large countable set.

edit: and 1.9999.... = 2. 🙂
 
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