size(s) of infinity

[OOBradm]

oh, and .9999999...... does not equal 1.

 

Originally posted by: OOBradm
oh, and .9999999...... does not equal 1.

1/3 = .33333333333...
2/3 = .66666666666...
3/3 = .99999999999... = 1

 

[Goosemaster]

Originally posted by: FallenHero

Originally posted by: OOBradm
oh, and .9999999...... does not equal 1.

1/3 = .33333333333...
2/3 = .66666666666...
3/3 = .99999999999... = 1

If 1 is a limit, then yes that does make sense because it cannot be reached....if it is a finite quantity, however, that is wrong.



At first I thought that they would be equal, using the reasoning above, if 1inch and 2inch are limits, then 1 inch is a limit within a larger limit...

0.....999999999999
0.....1.999999999


But in the end, there are no more points on the longer line as on the shorter line, as infinity is a concept and not a numerical value, and therefore, no numerically-based comparison can be reached.

 

[WinkOsmosis]

Yes there are more points on a 1" line than a 2" line. Just like there are more real numbers than whole numbers even though they are both infinite.

 

[DrPizza]

wow, I'm amazed at the number of people who actually knew anything about cardinality..... Yes, they both have the same cardinality (the same infinite number of points)

But, not all infinite sets are the same size of infinity... some infinities are more than other infinities....
(this should cause some headaches among the non-math majors )


Oh, and again, .99999..... DOES = 1. I ought to offer a prize to anyone who can successfully prove otherwise. (rigorously prove mathematically.... Anyone who proves the opposite can get published in any leading mathematics journal and be world famous)

 

[PowerMacG5]

Their are different levels of infinity. Ever hear of Aleph sub naught, and Aleph sub one?

 

[mfs378]

There are more points on the two-inch-segment.

The two-inch-segment is composed of two pieces, each of which identical to the one-inch-segment. So, for any specific point you choose on the one-inch-segment, you can find two identical points on the two-inch-segment (one in each of the one-inch parts). Thus, the two-inch-segment has twice as many points.

The fact that there are infinitely many points has no effect. Just define a distance between points delta, and find the ratio of points on one line versus the other. The answer is 2. Now let delta approach 0. The answer is independent of the size of delta. Q.E.D.

Simple.

 

[EyeMWing]

There are more points on the two inch segment.

the 1 inch line has [inf] points on it.
the 2 inch line has 2[inf] points on it.

I've always been told to use infinity as you would a variable (or pi, or other irrational number)

 

[XZeroII]

Infinity is infinity. You can't (by definition) have infinity * 2 or anything. Infinity is infinity is infinity.

 

[Hayabusa Rider]

Originally posted by: XZeroII
Infinity is infinity. You can't (by definition) have infinity * 2 or anything. Infinity is infinity is infinity.

Well, no. Consider the number line. Take a segment of the number line. Define one end as 0, and the other as 10. Now how many integers are there? Obviously a finite number. What about real numbers though? Well there are an infinite number no? But wait! Mathematic types know of something called hyperreals. There are more hyperreals than reals. So, there are an infinite number of reals, but a larger number of hyperreals which are also infinite. Therefore one infinity is "larger" than another.