What if science is wrong?

[spooky3 10]

To cover dosxuks' example there is what is known as a a "proper subset", even though they contain the same elements, they are still different sets.

 

The set of natural numbers is a proper subset of the set of rational numbers and the set of points in a line segment is a proper subset of the set of points in a line. These are examples in which both the part and the whole are infinite, and the part has the same number of elements as the whole; such cases can tax intuition.

http://en.wikipedia.org/wiki/Proper_subset

[dosxuk 10]

Except thatthere are no more integers to add to an infinite set of integers, the set already contains all of them, that is why it's called an infinite set.

 

...snip...

 

Please someone tell me if I've got that the right way round, I'm getting a headache

 

No, you're completely correct, set theory (as I agreed earlier), proves that one set contains more elements than the other, but, both sets are infinite in size - and multiples of infinity are still equal to infinity. Hence I said, due to the nature of infinity and the peculiar rules which apply to it, they can be mathematically proven to be the same length.

[spooky3 10]

No, you're completely correct, set theory (as I agreed earlier), proves that one set contains more elements than the other, but, both sets are infinite in size - and multiples of infinity are still equal to infinity. Hence I said, due to the nature of infinity and the peculiar rules which apply to it, they can be mathematically proven to be the same length.

 

Double infinity will always be twice the size of the original set of infinity.

[MrSmith 10]

They don't like infinity because it means they can't calculate an answer when they hit a term in an equation containing it, which means there is either something wrong with the theory they are using to make the calculation or they are missing a way of making the calculation which avoids the infinite term.

 

They understand infinity very well

 

Did you know for example there is more than one infinity ?

 

For example take the set of positive integers starting from zero and going on forever

 

This is a countably infinite set, so called because you can count each individual element, you'll never reach the end though because there isn't one.

 

Then take the set of real numbers, this is not a countably infinite set, you can't count each element one at a time, take any two real numbers which differ by as small an amount as you like and it's always possible to put another number between them, so you can't count the set, which makes that infinity larger than the earlier one.

 

Further there are even higher orders of infinity, I knew about the first two from school but the idea that there were more came as something of a surprise.

 

I found that fairly mind boggling, and I believe may have contributed to the nervous breakdowns suffered by Georg Cantor who found a way to make sense of the concept of infinity as an actual entity rather than something that could only be tended towards as a potential entity.

 

So mathematicians and physicists may not like the concept of infinity much, but they do understand it, and saying they are wrong about it just because they don't like it would be incorrect

 

Unless of course you can point to an opposing theory that explains the concept better.

 

 

Yes I did know all that, thanks, and I didn't say they didn't understand it.

[dosxuk 10]

Double infinity will always be twice the size of the original set of infinity.

 

Nope, because that implies that infinity has a size, which by it's very definition, it doesn't. Double infinity is equal to infinity. To state otherwise would imply that there were numbers larger than infinity, which there isn't.

[dosxuk 10]

Yes I did know all that, thanks, and I didn't say they didn't understand it.

 

You did say they were wrong about it though, implying that they don't understand it.

 

One thing that many scientists are wrong about, infinity, I know mathematicians and physicists hate the term.

[spooky3 10]

Nope, because that implies that infinity has a size, which by it's very definition, it doesn't. Double infinity is equal to infinity. To state otherwise would imply that there were numbers larger than infinity, which there isn't.

 

Look, even Lisa Simpson understands it!

 

If "infinity" is interpreted as any specific transfinite cardinal number κ ≥ \aleph_0 in cardinal arithmetic, then "infinity plus 1" = κ+1 = κ.

http://en.wikipedia.org/wiki/Infinity_plus_one

 

 

EDIT:

 

oops, wrong quote. Even though that last one states that afterwards it is infinity, but at the point of calculation it is theoretically larger.

 

In mathematics, infinity plus one has meaning for the hyperreals, and also as the number ω+1 (omega plus one) in the ordinal numbers and surreal numbers.

Edited April 19, 2012 by spooky3

[Mecky 10]

Right ot wrong, would it change anything? I certainly can't see it changing peoples' views.

[MrSmith 10]

Read the link, a subset and a superset of an infinite set can all be considered to have the same cardinality... Adding 1 to an infinite set doesn't make it larger.

 

This is why an infinite universe can still expand without getting bigger.

[MrSmith 10]

You did say they were wrong about it though, implying that they don't understand it.

 

Some scientist doesn’t think that an infinite universe is possible, whilst some scientists do think it’s possible, therefore some scientists are wrong about infinity. I should have said some instead of many, my bad sorry.

[HeadingNorth 11]

As you say, while we can prove that a set of all integers from 0..∞ has less items than a set of all real numbers from 0..∞ (or even a set of all real numbers between 0..1), but, both sets have ∞ items in them, and while of different lengths, both lengths are equal to ∞.

 

"Equal to infinity" is a meaningless phrase. Both sets have an endless number of items in them, but they are not "both equal to endless" because endless is not a number.

[HeadingNorth 11]

Lets say we've got the two sets - one of all integers, and one of all real numbers. There's currently more real numbers in our set than integers, so we add another load of integers to our set (∞+1 is a valid (albeight undefined) number, so we can add all the integral one of them to our integer set), until we've got as many entries as our real numbers set.

 

∞+1 is not a valid number; ∞ isn't a valid number, it's a quality.

 

You can perform arithmetical operations on it, but the answers you get won't obey the rules of arithmetic because you're not working with numbers.