As I said before, you weren't using a contradiction proof in a valid way. You weren't opposing anything.
So you want to show that they don't intersect at all?
Wait what? When simultaneously equating two functions one finds the points at which the functions intersect on a graph. Sure, you can find that they don't intersect but they can't intersect at all points. If you drew two functions that intersected at every point you would in fact have only drawn one function.
No. Say I have f(x)=x+5 and g(x)=x^2:
As equations y=x+5 and y=x^2. Equating them gives x^2=x+5 or X^2 - x - 2=0. This is then factorised => (x-2)(x+1)=0 which gives x=2 or x=-1. When x=2, y=4 and when x=-1, y=1 so the solution is (-1,1) or (2,4). This means that the two functions intersect at two points (-1,1) or (2,4).
If I decide that I'm going to 'let x=7' for example:
y=7^2 =>49
y=7+5 =>12
49≠12. I think we can agree on that much
![Stick Out Tongue :p :p](/styles/default/xenforo/smilies/tongue.gif)
. Because they don't equal I've proven that when x=7, the y values are different thus they do not intersect (cross or touch). I haven't however proven that the two functions contradict or that they don't intersect. Just that they don't intersect at the point where x=7.
What statement?? You have to assert a statement before you can contradict it. Just having two equations and sticking random numbers into them serves no purpose.
So this entire thing is because you neglected to read.
b is the slope.
Since both of the slopes are one, the lines are parallel, therefore, the lines must intersect at either all points or no points.
They are parallel lines, I proved that, therefore they must intersect at all points or none, that is the nature of parallel lines.
Capish?
No, your functions aren't parallel.
If you're gonna comment on a mathematical proof, you need to read the actual proof.
I can see where Crash is coming from; you're making a fundamental mistake in the way you go about describing what constitutes proof.
In science, nothing is ever proven. Facts are weaved together to form theories, this is basic scientific knowledge. We deal with probabilities, not concrete proof; some probabilities just happen to be insanely greater by orders of several magnitudes when compared with others (I.E. the existence of a black swan vs. the origin of the universe).
The only time anything can ever be "proven" is in mathematics. Math deals with "proofs", science deals with probabilities.
You're wrong, while you're correct in practice, I'm taking it from a technical logical point of view.
Firstly, that set of posts was primarily dealing with a pure logic prospective, in other words MATH. I did a little burb on science at the end, but my PRIMARY commentary was on logic.
Secondly, as far as science goes, you only cannot prove things or disprove it when you talk about it in the practical sense (namely, what science is built to examine). In the technical logical sense, you're proving and disproving things all the time.
Science is primarily concerned with commentary on:
A. Positive Universal Statements.
B. Negative existential statements.
A is "for all", and B is "x does not exist",
In the framework of science, it's for all practical senses impossible to prove that something applies universally, and it's equally impossible to prove something does not exist.
However, you can prove another statement, the positive existential statement, the positive existential statement is the "facts" that you refer to, those are the observations, they are proven all the time because the observance of one proves the existential statement.
In the same sense, it is impossible to practically disprove that something exists (the main issue here being that the positive universal statements are impossible to prove).
However, you can disprove universal statements, that happens all the time. The process is called "rejecting the null hypothesis" (I know that you know what this is, but just explaining what it is from a technical logical prospective).
So, I know that this will come up very rarely, but it's important to have the technical background clear because it does come up, and realistically having the terminology right helps in those situations.
Really, how much more effort does it take to say, "negative existential statements are impossible to prove" then "negatives are impossible to prove"? Just type the extra two words.
Yes, technically when he "proved" something it was only based on "math", not "science"...
But I don't think he was trying to say science can prove something, but rather it was in response to a different statement someone said: "You cannot prove something does not exist".
If you think of it that way he did show that's possible.
-blazed
Pretty much.
But also commenting on science from a technical logic prospective, the scientific method does prove and disprove things, they're just not the things science is talking about.
But you really can't prove that either, without making the same assumptions we have to make to prove something does exist.
That assumption is assumed for any debate that is not philosophical or supernatural in nature, every debate has it's preconceptions (namely the scenario), and implicit in those preconceptions is what needs to exist for the debate to occur exists.