Now they just have to show how this "early atmosphere" with 40% hydrogen can be used in an experiment similar to the Stanley Miller experiment to produce amino acids.... (the Miller expt didn't have 40% hydrogen).
And then you have to show how these amino acids can form proteins... and how DNA can arise.
Amino acids have eve been found on meteor rocks... But just because you have the building block for life, it still doesn't explain how life formed in teh first place. Just as having bricks doesn't explain how houses are built.
I'm not saying that infinity infinity. But one set is strictly larger than the other. Thus, one infinite set is larger than another infinite set. This is set theory.
I hope the links help a bit... if you know anyone who knows set theory well you can talk to them... and maybe number theory, I'm not too sure about that (I've only taken one number theory course so far).
I think we're talking about different concepts of infinity.
The set of all natural numbers N is a proper subset of the set of all real numbers R. So in the lanauge of set theory, R is strictly larger than N.
>>If I had a computer that could count an infinite number of objects in one second, I could count all the positive integers (an infinite number) in one second. How long would it take to count all the fractions between 1 and 2 (an infinite number)? One second. How long to count all the possible fractions (an infinite number) between all the positive integers (another infinite number)? One second.
You are already assuming all infinite sets to be the same size... so it doesn't show anything.
Going back to set theory, there are two types of infinite sets, countable and uncountable. The set of real numbers would be uncountable, while the set of natural numbers would be countable. The set of real numbers is larger than the set of natural numbers, you cannot argue against that.
An example I gave before is real and natural numbers... the set of all natural numbers N is a proper subset of the set of all real numbers R, but R is not a subset of N. So in the language of set theory, R is the larger set containing N.
>>but unless one infinitely large set can be larger than another infinitely large
Yes, some infinite sets are larger than the other. You can measure the sizes of sets using 1-1 correspondance between elements in the set to positive integers. The example I gave is real numbers vs. natural numbers. If you think about it, the set of all real numbes contain the set of al natural numbers... but not the other way around.
Which definition are you using exactly? Just curious
When it comes to the set theory, we need to define countable infinity and uncountable infinity.
By larger I don't mean that the value of an infinity is larger than the other. But a particular infinite set can be a larger set than another infinite set (eg. real numbers vs. natural numbers). The sizes of sets are compared using the concept of 1-1 correspondance.
Of course in terms of real analysis, infinity is not a number... so it would be absurd to say one is larger than the other. You are quite right about that.
It is not erroneous. While it may not be intuitive, it is correct. I have learned this in both my stats and combinatorics course during my second year at University of Waterloo.
There are different sizes of infinity.
In the context of number system, infinity does not exist... it cannot be treated as a number.
In the context of measuring sizes of sets, infinity does exist, and some infinity is larger than others. Say you have the set of all real numbers R, and the set of all natural numbers N. Clearly, R and N are both infinite in size, but the size of R is larger than that of N.
It is a weird concept at first.;)
Slashdot Mirror
The whole thing was done using chalks.
Actually, the Roman emperor used some thumb gesture, and no one knows what it is.
The thumbs up and thumbs down is just something people see in movies, and assumed is true.
Now they just have to show how this "early atmosphere" with 40% hydrogen can be used in an experiment similar to the Stanley Miller experiment to produce amino acids.... (the Miller expt didn't have 40% hydrogen). And then you have to show how these amino acids can form proteins... and how DNA can arise. Amino acids have eve been found on meteor rocks... But just because you have the building block for life, it still doesn't explain how life formed in teh first place. Just as having bricks doesn't explain how houses are built.
You have 20% of a single digit figure. 20% of 9 is 1.8.
>>multiply their value by 2
o ld=1&commentsort=0&tid=156&mode=thread&cid=1078491 0
You've just put the set under a transformation... so you're actually ending up with a different set (ie. the set of all positive integers)
I think miskatonic alumnus has posted a pretty nice reply here: http://slashdot.org/comments.pl?sid=129086&thresh
Although I'm not too sure how much these links and replies help you, I do hope they at least help a bit. =)
I'm not saying that infinity infinity. But one set is strictly larger than the other. Thus, one infinite set is larger than another infinite set. This is set theory.
>> If that is the definition of an uncountable set then all infinite sets are uncountable
m l - this page talks about different sizes of infinity
That's not true... countable and uncountable sets both refer to infinite set.. but that's another topic.
>>If you (or anyone else) can give links to information on this topic I would be grateful.
http://en.wikipedia.org/wiki/Infinity - I love wikipedia.. read the part about infinity in set theory, it talks about countable and uncountable sets.
http://mathforum.org/library/drmath/view/53352.ht
I hope the links help a bit... if you know anyone who knows set theory well you can talk to them... and maybe number theory, I'm not too sure about that (I've only taken one number theory course so far).
I think we're talking about different concepts of infinity.
The set of all natural numbers N is a proper subset of the set of all real numbers R. So in the lanauge of set theory, R is strictly larger than N.
>>If I had a computer that could count an infinite number of objects in one second, I could count all the positive integers (an infinite number) in one second. How long would it take to count all the fractions between 1 and 2 (an infinite number)? One second. How long to count all the possible fractions (an infinite number) between all the positive integers (another infinite number)? One second.
You are already assuming all infinite sets to be the same size... so it doesn't show anything.
Going back to set theory, there are two types of infinite sets, countable and uncountable. The set of real numbers would be uncountable, while the set of natural numbers would be countable. The set of real numbers is larger than the set of natural numbers, you cannot argue against that.
Two infinite sets can have diferent sizes.
An example I gave before is real and natural numbers... the set of all natural numbers N is a proper subset of the set of all real numbers R, but R is not a subset of N. So in the language of set theory, R is the larger set containing N.
>>but unless one infinitely large set can be larger than another infinitely large
Yes, some infinite sets are larger than the other. You can measure the sizes of sets using 1-1 correspondance between elements in the set to positive integers. The example I gave is real numbers vs. natural numbers. If you think about it, the set of all real numbes contain the set of al natural numbers... but not the other way around.
Which definition are you using exactly? Just curious
When it comes to the set theory, we need to define countable infinity and uncountable infinity.
By larger I don't mean that the value of an infinity is larger than the other. But a particular infinite set can be a larger set than another infinite set (eg. real numbers vs. natural numbers). The sizes of sets are compared using the concept of 1-1 correspondance.
Of course in terms of real analysis, infinity is not a number... so it would be absurd to say one is larger than the other. You are quite right about that.
It is not erroneous. While it may not be intuitive, it is correct. I have learned this in both my stats and combinatorics course during my second year at University of Waterloo.
m l
For more info, I found this page using Google: http://mathforum.org/library/drmath/view/59138.ht
There are different sizes of infinity. In the context of number system, infinity does not exist... it cannot be treated as a number. In the context of measuring sizes of sets, infinity does exist, and some infinity is larger than others. Say you have the set of all real numbers R, and the set of all natural numbers N. Clearly, R and N are both infinite in size, but the size of R is larger than that of N. It is a weird concept at first. ;)