The Math Thread!
- Thread starter Argetlam
- Start date
OHHHH. S = D/T I was thinking something else...
You said this:
Total Distance = 2 Miles
Total Time = 1/30 + 1/90 Hour = 2/45 Hour
Wouldn't it be correct that its 60 because 1/30 + 1.90 is 2/120. or am I confusing t with something else, making:
You said this:
Total Distance = 2 Miles
Total Time = 1/30 + 1/90 Hour = 2/45 Hour
Wouldn't it be correct that its 60 because 1/30 + 1.90 is 2/120. or am I confusing t with something else, making:
1 1
X
30 90
So, then it would be 1/3... err.X
30 90
Let:
p = Finding $1
q = Going to the movies
"If I find $1, I'll go to the movies." means p -> q
"I found $1." means p
Modus Ponens (which is a valid rule of inference) says that [(p->q) ^ p] -> q, so q must be true. So I'll go to the movies.
p = Finding $1
q = Going to the movies
"If I find $1, I'll go to the movies." means p -> q
"I found $1." means p
Modus Ponens (which is a valid rule of inference) says that [(p->q) ^ p] -> q, so q must be true. So I'll go to the movies.
Derivatives are fun. Hit me.
- "It is raining right now."
- "It is 10 PM right now."
We assign these true/false proposition to letters, like p and q. Each letter would mean a certain statement, depending on what you set it to. So if we set p to be the proposition that "It is raining right now," then p is true if it is raining right now, or false otherwise. Am I making sense so far?
Okay, let's start from the basics. First, let's define a proposition: A proposition is a fact that is either true or false. For example:Snivylover555 said:
- "It is raining right now."
- "It is 10 PM right now."
We assign these true/false proposition to letters, like p and q. Each letter would mean a certain statement, depending on what you set it to. So if we set p to be the proposition that "It is raining right now," then p is true if it is raining right now, or false otherwise. Am I making sense so far?
Now, we have special operators for these propositions, I'll introduce the basic three:
AND Operator (Sometimes written as &)
p ^ q, where "^" is the AND Operator. p ^ q is true if and only if both p and q are true. If either p or q are false, then p ^ q is false.
OR Operator (Sometimes written as |)
p V q, where "V" is the AND Operator. p V q is true if either p or q are true. If BOTH p and q are false, then p V q is false.
NOT Operator (Sometimes written as ~)
¬p, where "¬" is the NOT Operator. ¬p is true when p is false, and ¬p is false when p is true. It's basically the opposite of everything.
AND Operator (Sometimes written as &)
p ^ q, where "^" is the AND Operator. p ^ q is true if and only if both p and q are true. If either p or q are false, then p ^ q is false.
OR Operator (Sometimes written as |)
p V q, where "V" is the AND Operator. p V q is true if either p or q are true. If BOTH p and q are false, then p V q is false.
NOT Operator (Sometimes written as ~)
¬p, where "¬" is the NOT Operator. ¬p is true when p is false, and ¬p is false when p is true. It's basically the opposite of everything.
I've prepared you for this: The Implication:
The implication operator means that one thing leads to another. Hence it's an arrow sign: →
The statement: p→q means that if p is true, then q must be true. Going back to glaceon's problem, he wrote:
p = Finding $1
q = Going to the movies
He said that if he finds $1, then he'll go to the movies, so p→q, because if p (he finds $1) is true, the q (he will go to the movies) must be true. He then said that p is indeed true. So q is true and he will go to the movies. This is called Modus Ponens (no you don't have to remember that, lol).
Now let's move on to glaceon's most recent question:
p = Finding $5
q = Buying a car
Again, he said that if he gets $5, then he'll buy a car, so p→q. But this time, he didn't get the money, so p is false, not true. Does that mean q is false too? People who say that are wrong and commit a fallacy called "Denying the Hypothesis". If p is false, q is not necessarily false too. Someone might help him pay the car, he could find a discount, or something that would let him buy a car even if he didn't find the $5 he wanted.
So that's it, lol.
The implication operator means that one thing leads to another. Hence it's an arrow sign: →
The statement: p→q means that if p is true, then q must be true. Going back to glaceon's problem, he wrote:
So we assign the propositions as so:glaceon said:
p = Finding $1
q = Going to the movies
He said that if he finds $1, then he'll go to the movies, so p→q, because if p (he finds $1) is true, the q (he will go to the movies) must be true. He then said that p is indeed true. So q is true and he will go to the movies. This is called Modus Ponens (no you don't have to remember that, lol).
Now let's move on to glaceon's most recent question:
We assign the propositions as so:glaceon said:
p = Finding $5
q = Buying a car
Again, he said that if he gets $5, then he'll buy a car, so p→q. But this time, he didn't get the money, so p is false, not true. Does that mean q is false too? People who say that are wrong and commit a fallacy called "Denying the Hypothesis". If p is false, q is not necessarily false too. Someone might help him pay the car, he could find a discount, or something that would let him buy a car even if he didn't find the $5 he wanted.
So that's it, lol.