Is there a relation between the fact that the derivative of x^2 is 2x and that the difference between 1,4,9,16, ... is 3, 5, 7, 9, ...?
And why is the difference always 2?
I understand now, it's the direction that is negative, not the magnitude.
Why is it better to think of acceleration as Δv/Δt?
I guess it just a matter of which is more intuitive/elegant, but maybe there is another reason; is there?
I think we can't have a negative displacement. Is that right?
Acceleration: the change in displacement / change in time squared
Since displacement can't be negative, and time can't be negative, acceleration also can't be negative.
But I know (it's in the books) that when we have decreasing...
In a try to test my knowledge of Newton's laws, I have posed the following question to myself.
My attempt:
(The arrows indicate direction.)
I have been informed that the solution is invalid, and that the question itself is wrong. Can you tell me why the problem is wrong/invalid?
Someone...
That's what I was trying to understand.
Saying "innocent until guilty" doesn't help. It still means that there is a 50% chance it is "not innocent"; as you put it, the implication alone when 'p' is false gives us 0 information, it has to be accompanied with more information. I still need to...
If it's not random, then how are the last two truth values chosen?
If I tell someone "you are innocent until proven guilty", that doesn't mean he really isn't guilty. He could be guilty, but "considered" not guilty. And he still could be innocent. I can't conclude what he really is.
A theorem can be proven according to axioms, and axioms can be wrong. Regardless of that, I just don't want to take this in consideration (or discuss it), that's why I said "Aside from the fact that ...".
"I'm asking if the randomness of the (last two) values given to "implication" lead to...
As HallsOfIvy puts it "innocent until proven guilty". "innocent until proven guilty" means, in reality, we don't know if the truth-value of FT and FF are T and T respictively. What we do is "consider" them True. Why did we chose them to be True? (We choose them to be True randomly)...
I think I understood the point. And if I did understand correctly, this is another issue that is related to theorems.
I'm asking if the randomness of the (last two) values given to "implication" lead to theorems being possibly/potentially incorrect. Aside from the fact that the prepositions...
"In either case, you certainly cannot say that what your teacher told you at the beginning of the course was not true."
So, we don't have basis for assigning the value T for the last two cases.
"I don't know where you got the idea that we "randomly" choose anything. I think of it rather as...
I understand that we just have to fill the last two raws in the truth table with any value, and that we randomly chose True, and that the value True makes matters easier sometimes (I don't know an example of that, but I read that somewhere).
But the question is, since mathematics is tied to...
The webpage in the link you've given says:-
The function is:-
0 when x < 0,
1/2 when x = 0,
1 when x > 0.
But here: http://simple.wikipedia.org/wiki/Heaviside_Function, defines the function as:-
1 when x => 0,
0 when x < 0.
To begin with, which should I follow?
What does "H" mean?!
I have this question in my assignment paper:-
8. Sketch the graph of:
(a)
y = |2x − 2|;
(b)
y = 2H(x − 4)
(a) is obvious, but how do I sketch (b)? Does "H" stand for some specific constant?
Hi,
I need two book recommendations for each of the following, one classical (i.e. covers the subject in detail, more like a reference, and influential if such book exists) and one as a quick study material.
The topics:-
1) Algebra
2) Geometry
3) Trigonometry
4) Calculus
Thanks.