It's got nothing to do with military vs. civilian. Airliners depressurize occasionally. But they fly low enough that simple airmasks can suffice while the pilots do an emergency descent into the range of breathable atmosphere. You fly high enough and an airmask isn't gonna do the trick anymore.
Yes the rationals are a field, in fact they're ordered too. That is why the field axioms and the order axioms are not enough to fully describe the reals. That is why you need the completeness property which is a property that the rationals do not have.
For something to be a fact it has to be true and you have to know that it's true. The problem isn't that things aren't true, the problem is that you can't know anything with 100% accuracy.
Yes, I missed it, I only skim these forums. So as you haven't objected to any of the points above am I to take it that you've changed you mind and will accept that infinity + finite = infinity?
Infinity does not "have" a set, that statement doesn't mean anything. Sets have a cardinality, not the other way around. And what exactly do you think is illogical about my previous example? I'll break it down for you:
a) The set {0, 1, 2, 3,...} has an infinite number of elements.
b) The set {1, 2, 3,...} has an infinite number of elements.
c) The set {0} has 1 element.
d) The set {0} union {1, 2, 3,...} is the set {0, 1, 2, 3,...}.
e) The intersection of the set {0} and the set {1, 2, 3,...} contains no elements.
f) When two sets are disjoint (no elements in the intersection) the cardinality of their union is the sum of their cardinalities.
g) So card{0, 1, 2, 3,...} = card{0} + card{1, 2, 3,...}
h) Thus infinity + 1 = infinity
Now you've said you disagree with (h), I've laid out the reasons why I feel I'm justified in concluding (g). So please indicate what step you believe to be incorrect and why.
Also, I'll ask you again. Do you have a referance for the term "affinity" or did you invent it yourself?
Did you invent this term "affinity" or can you provide a referance? Being a math person it's a pet peeve of mine when people decide to make up math to support their philosophical leanings. Math is definitions and logic, not hand waving and mysticism. If the math doesn't line up with your views you're free to say that math doesn't accurately model whatever system you're talking about; you're not free to make up bad math.
If you would like an example of infinite + finite = infinite just look at the natural number plus 0. {1, 2, 3,...} union {0} = {0, 1, 2, 3,...}. In terms of cardinality we have aleph null + 1 = aleph null, thats infinity + finite = infinity.
So yes, the statement IS in fact TRUE for numbers.
What the hell is affinity? I'm a mathematics major and I've never heard that.
There's nothing wrong with saying that if x is a finite number and y is infinity then x + y = infinity, at least nothing more then the obvious fact that it's not very precise mathematically. It can easily be made precise by the notion of convergence and there are no surprises when you do so, you get pretty much exactly what you expect.
Your statement on set theory is completely correct and mathematically precise.
The statement about the addition of infinite numbers is also correct and can be made mathematically precise with limits. But limits are essentially a very painful way of making what we think of as an intuitive notion precise, which is why once we've proven a statement using limits we immidiately stop using limits when we state the result.
They didn't. He hasn't gone public with the device yet. There's a reason for peer review. Theese types of issues can be extreemly nuanced and difficult to analyse. The scientific community as a whole needs to take a look at it, not just a couple of "independant scientists." When that happens, if it's found that the claim is true, you can bet that every scientists in this field is going to be talking about it. It's not going to get swept under the rug, that's absurd.
They're not taking QM as scripture, they just have confidence in it because up till now it's always been true to an unbelievable degree of accuracy. If someone told you the law of gravity was wrong and they had found an object that fell upward, would you instantly believe them? No, you would want to see proof. That's not to say it's impossible, maybe quantum mechanics is wrong. But the chances are it's not. Scientists believe in science and there's science behind the tests that have been made of QM. When/if this guy comes out with his device the scientists will be able to take a look at in and see what's really going on. But until they get to do that it's only reasonable that they maintain confidence in QM which is scientifically very well established.
Very true, but the problem is that those wild ideas, even at their conception, are testable in principle. As you mention Einstein I will use him as an example. The theory of general relativity went many years without being solidly confirmed by experimental evidence. That is because we didn't have instruments or methods that were capable of testing the differences between General Relativity and Newtons theory. But there were differences. You plug the same numbers into both theories and you get two different numbers out, so it was testable in principle, and that makes it scientific. But if you postulate a creator, that is not testable. There is no test you can preform which will solidly differentiate between these two theories. ID makes no predictions that are testable in principle. That is why it's not considered science.
Outright refusal to study any valid scientific theory on the basis that it involves a divine being is teaching atheism.
The point here is that there is no such thing as a valid scientific theory that involves a divine being. Those theories are not testable and hence are not science.
That is not the gist of it, that is completely skewed.
For starters scientists aren't whining, they're speaking up about a legitimate problem. Science and religion are two seperate things, they should not be confused, and teaching ID in a science class is definitly a confusion.
Secondly science doesn't say that god didn't create man. Science says that it's possible that man evolved from apes. It then looks at the evidence and see's that not only does nothing rule this out as a possibility, but there are several things that are conveniently explained by it, leading many to believe that it's true. It could be false, you never really proove anything in science, there is always the possibility that your wrong. But even if it is true. Science doesn't rule out god having a hand in it. Maybe god created the apes with the intention that they evolve into man, that to me could be validly described as "god creating man" or maybe god created the creature that evolved into the ape, or the creature that evolved into the creature that... and so on. Hell, maybe all god did was kickstart the universe at the beginning in such a way that he knew all of this would come to be, or maybe god created the universe yesterday and created all our memories and the fossile record along with it. Or maybe god doesn't exist and there is a purely naturalistic explanation for it all. Who knows. The point here is that there is no test that we can develope to distinguish between any of those scenarios, that's why they fall under the jurisdiction of religion and philosophy, not science.
Until ID makes firm predictions that are testable in princible it is most certainly not science. It's not whining to point out the truth.
The brand has entered my thoughts in a negative way. Thoughts of that brand are inherrently linked to thoughts of annoyance and aggrivation. So it certainly doesn't benifit the company that I saw their ad.
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It's got nothing to do with military vs. civilian. Airliners depressurize occasionally. But they fly low enough that simple airmasks can suffice while the pilots do an emergency descent into the range of breathable atmosphere. You fly high enough and an airmask isn't gonna do the trick anymore.
That's called dynamic range, and it's a good thing.
Yes the rationals are a field, in fact they're ordered too. That is why the field axioms and the order axioms are not enough to fully describe the reals. That is why you need the completeness property which is a property that the rationals do not have.
Fact and truth don't mean exactly the same thing. Don't confuse them.
Be warned, what I'm about to say may shock people. ID and the FSM were taught to me in school... in my philosophy class.
The problem isn't that people want students to learn about ID, the problem is that people want students to be taught to believe in ID.
For something to be a fact it has to be true and you have to know that it's true. The problem isn't that things aren't true, the problem is that you can't know anything with 100% accuracy.
Yes, I missed it, I only skim these forums. So as you haven't objected to any of the points above am I to take it that you've changed you mind and will accept that infinity + finite = infinity?
Infinity does not "have" a set, that statement doesn't mean anything. Sets have a cardinality, not the other way around. And what exactly do you think is illogical about my previous example? I'll break it down for you:
...} has an infinite number of elements.
...} has an infinite number of elements.
...} is the set {0, 1, 2, 3, ...}.
...} contains no elements.
...} = card{0} + card{1, 2, 3, ...}
a) The set {0, 1, 2, 3,
b) The set {1, 2, 3,
c) The set {0} has 1 element.
d) The set {0} union {1, 2, 3,
e) The intersection of the set {0} and the set {1, 2, 3,
f) When two sets are disjoint (no elements in the intersection) the cardinality of their union is the sum of their cardinalities.
g) So card{0, 1, 2, 3,
h) Thus infinity + 1 = infinity
Now you've said you disagree with (h), I've laid out the reasons why I feel I'm justified in concluding (g). So please indicate what step you believe to be incorrect and why.
Also, I'll ask you again. Do you have a referance for the term "affinity" or did you invent it yourself?
If you would like an example of infinite + finite = infinite just look at the natural number plus 0. {1, 2, 3, ...} union {0} = {0, 1, 2, 3, ...}. In terms of cardinality we have aleph null + 1 = aleph null, thats infinity + finite = infinity.
So yes, the statement IS in fact TRUE for numbers.
What the hell is affinity? I'm a mathematics major and I've never heard that. There's nothing wrong with saying that if x is a finite number and y is infinity then x + y = infinity, at least nothing more then the obvious fact that it's not very precise mathematically. It can easily be made precise by the notion of convergence and there are no surprises when you do so, you get pretty much exactly what you expect.
Not neccesary actually.
Your statement on set theory is completely correct and mathematically precise. The statement about the addition of infinite numbers is also correct and can be made mathematically precise with limits. But limits are essentially a very painful way of making what we think of as an intuitive notion precise, which is why once we've proven a statement using limits we immidiately stop using limits when we state the result.
Try reading the article. Then look at what you wrote.
They didn't. He hasn't gone public with the device yet. There's a reason for peer review. Theese types of issues can be extreemly nuanced and difficult to analyse. The scientific community as a whole needs to take a look at it, not just a couple of "independant scientists." When that happens, if it's found that the claim is true, you can bet that every scientists in this field is going to be talking about it. It's not going to get swept under the rug, that's absurd.
They're not taking QM as scripture, they just have confidence in it because up till now it's always been true to an unbelievable degree of accuracy. If someone told you the law of gravity was wrong and they had found an object that fell upward, would you instantly believe them? No, you would want to see proof. That's not to say it's impossible, maybe quantum mechanics is wrong. But the chances are it's not. Scientists believe in science and there's science behind the tests that have been made of QM. When/if this guy comes out with his device the scientists will be able to take a look at in and see what's really going on. But until they get to do that it's only reasonable that they maintain confidence in QM which is scientifically very well established.
And how do you propose we test them?
Very true, but the problem is that those wild ideas, even at their conception, are testable in principle. As you mention Einstein I will use him as an example. The theory of general relativity went many years without being solidly confirmed by experimental evidence. That is because we didn't have instruments or methods that were capable of testing the differences between General Relativity and Newtons theory. But there were differences. You plug the same numbers into both theories and you get two different numbers out, so it was testable in principle, and that makes it scientific. But if you postulate a creator, that is not testable. There is no test you can preform which will solidly differentiate between these two theories. ID makes no predictions that are testable in principle. That is why it's not considered science.
If you can't see that ID is badly disguised creationism then I believe it is you that is lacking understanding.
The point here is that there is no such thing as a valid scientific theory that involves a divine being. Those theories are not testable and hence are not science.
For starters scientists aren't whining, they're speaking up about a legitimate problem. Science and religion are two seperate things, they should not be confused, and teaching ID in a science class is definitly a confusion.
Secondly science doesn't say that god didn't create man. Science says that it's possible that man evolved from apes. It then looks at the evidence and see's that not only does nothing rule this out as a possibility, but there are several things that are conveniently explained by it, leading many to believe that it's true. It could be false, you never really proove anything in science, there is always the possibility that your wrong. But even if it is true. Science doesn't rule out god having a hand in it. Maybe god created the apes with the intention that they evolve into man, that to me could be validly described as "god creating man" or maybe god created the creature that evolved into the ape, or the creature that evolved into the creature that... and so on. Hell, maybe all god did was kickstart the universe at the beginning in such a way that he knew all of this would come to be, or maybe god created the universe yesterday and created all our memories and the fossile record along with it. Or maybe god doesn't exist and there is a purely naturalistic explanation for it all. Who knows. The point here is that there is no test that we can develope to distinguish between any of those scenarios, that's why they fall under the jurisdiction of religion and philosophy, not science.
Until ID makes firm predictions that are testable in princible it is most certainly not science. It's not whining to point out the truth.
You seem to be implying that I would care...
That is such a bad translation...
No, c 1 is valid. The problem is that that's only valid when the denominator of the fraction is positive.
A perscription isn't required. I don't have a perscription.
The brand has entered my thoughts in a negative way. Thoughts of that brand are inherrently linked to thoughts of annoyance and aggrivation. So it certainly doesn't benifit the company that I saw their ad.