Math Problem, Arguement with the teacher. Easy Logic.

[Mike Laserbeam]

Actually, no.
In fact, you're so wrong, you made me register an account to correct you.

Proof by induction works like this:

You *prove* that your claim is correct for n=1 (or where ever else you start), then you *prove* that, if the claim is correct for n=k, it's also correct for n=k+1 (or some other step size, depending on the problem).

If you combine those two *proven facts* that the claim is correct for all n, since if it's correct for 1 it's also correct for 2. And if it's correct for 2 it's also correct for 3. Imagine, if you will a row of dominoes falling, each one pushing over the one after it.

(Apologies if unclear, not a native speaker)

The first one isn't an assumption, it is the base case. You prove this with normal mathematics. Its usually used to prove formulas to explain mathematical patterns in numbers, so first you work out the first few values of the pattern, then create a formula then use the proof by induction to prove the formula for all values of the pattern.

Right right, basis case n=1, inductive step assume true for n=k, show that true for n=k+1, there's an assumption which was my main point.

 

[YouBecame]

The whole of maths is pretty much assumption.
As is everything.
It could be that you'll get better anyway, so that would be true.

I don't understand how the hole of math is a assumption, I have decided that using mathematics is the best way to determine reality which is the nothing less than the absolute truth of things. How can you assume the truth of something when you could be wrong, this makes it non absolute and pointless to consider as fact.

Theorems are the cornerstone of mathematical discovery and are build upon axiomic truths: Things assumed to be true just because they are obvious. Inct, there have been examples where a convoluted axiom has led to odd mathematics, for example Euclid in his treatise The Elements, assumed something about triangles which can be untrue if you inscribe the triangle on a sphere. Mathematicians like Newton were left assuming that Calculus had some reason to work, just because their methods seemed to give plausable answers. Hundreds of proofs were constructed upon an unproven theory just because they hoped the theory was true.

In essence, you would be surprised jsut how much we assume to know in mathematics.

 

[Drug Crazed]

And it is useful, usely is not a word.

And I'm doing Computer Science with Maths and therefore am allowed to make typos.

snip

Apologies, I get easily frustrated at stuff like that. In reply, its a sad fact about the teaching, but I've always been lucky with my teachers (though we never did logic in maths).

If I were a lesser man, I'd make a joke about implication.

I'm going to agree with your teacher, in the sense that you should just accept it and get on with something else.

That's the worst thing that could possibly be done. If you don't understand it you'll have a hell of a time when you see it in-depth in a future time (like college or whatever it is you Americans call it ). I know that after me not understanding a good 50% of Mechanics 1, when Mechanics 2 referenced M1 I struggled an awful lot. Its easier to be understood now, while its fresh than to have incorrect things for future problems.

Imagine if you didn't understand why 2+2=4, and why it didn't equal 5. Then when you met multiplication you'd have difficulties. I know I've chosen something basic that most people do, but you get my drift

 

[Singletap]

I have a better example:

If I kill you today then you will die today. Obviously true.
If I kill you today then you will not die today. Obviously false.
If I don't kill you today then you will die today. True, as you may get hit by a truck or something.
If I don't kill you today then you wil not die today. True, as you may not get hit by a truck or something.

Bit of a morbid example, but it was the first thing that came into my head. Logic like this is really meant for absolutes, but True and False don't mean what they should.

True = Not False
False = Immposible

I agree that logic like this is dumb, even in CompSci ifThenElse has a totally more relevant use.

Well this would be a lot easier if someone told me that true is not true but it is not false instead. I assumed that true meant that it happened because of the if.

 

[Drug Crazed]

Why make the biggest assumption that the medicine will help?

The real problem in mathematics is that we have to have real life examples that can contridict the fabric of reality that we know.

So, ignore what the question is actually saying. Treat them as A and B. Then it makes sense.

 

[Liquid Paradox]

Well this would be a lot easier if someone told me that true is not true but it is not false instead. I assumed that true meant that it happened because of the if.

that is the I it should be. True should be "absolute" while false should be "not true", but this is not the way things are done.

 

[Singletap]

I have a better example:

If I kill you today then you will die today. Obviously true.
If I kill you today then you will not die today. Obviously false.
If I don't kill you today then you will die today. True, as you may get hit by a truck or something.
If I don't kill you today then you wil not die today. True, as you may not get hit by a truck or something.

Bit of a morbid example, but it was the first thing that came into my head. Logic like this is really meant for absolutes, but True and False don't mean what they should.

True = Not False
False = Immposible

I agree that logic like this is dumb, even in CompSci if... then... has a totally more relevant use:

if iKillYou
then youDie

So the 1st is true, the 2nd is false and the other two depend on what other stuff you stick in it.

I thought it was
False=False
True=Maybe

Or Undefined=maybe/no idea.

True would=undefined in your case though.

 

[Danny Ocean]

Why make the truth table if it could be wrong. What if it ends up being true and it is actually false wouldn't that create a problem in a code?

It doesn't really matter if the medicine helps or not because this is just a thought exercise.

You could just as easily construct a truth table from any other premise. Perhaps it would be easier for you if I re-word it like this:

"It is the case that if you take your medicine then you will feel better."

It doesn't matter that the medicine may or may not work. You are being given a truth and being told to conclude from it using a truth table.

In the real world you'd determine the validity of the above statement using scientific tests. For your logic class, however, we can safely take it as a given because it's not being used to make any decisions beyond the classroom.

I understand you're getting worked up over the above statement because it's just as much an assumption to take it as a given that the medicine works as to take it that it doesn't. Let's pursue this, shall we?

Say that scientific trials confirm that the medicine works. The premise is valid.

Say that scientific trials confirm that the medicine does not work. The premise is invalid.

You are no longer working on an assumption. Or are you? You see, even those scientific trials operate on assumptions in maths and in the way we perceive the world. When it comes down to it, we can't really know anything other than the existence of our own consciousness. As Descartes said, "I think, therefore I am."

It is pointless, therefore, to get all worked up over this particular premise, and instead just accept that it's OK to take it as a truth for the purposes of the exercise. You're going to hit the wall of unknowable reality eventually as long as you apply your logic consistently.

So just accept the inconsistency and enjoy the thought exercise.

All of the above is a different kind of logic, I think. I don't know how computer code differs. The above may or may not be relevant to you.

True would=undefined in your case though.

He states that:

True= ¬False
False= ¬Possible.

True = ¬False = ¬Possible

True = ¬¬Possible.

True = Possible.

The probability is a different issue. All we need know is if it is at all possible.

 

[Shynobee]

You are making the biggest assumption that the medicine will not help.

What you need to understand is that school math lives in a bubble. The ways of reality and actual life do not apply. You take what is given, and nothing else. In other words, you are reading too deeply into the problem. You can't do that in school math.

Why make the biggest assumption that the medicine will help?

Its not an assumption, its given in the problem.

The initial sentence was "If you take the medicine, then you will get better."

Thus, we are given by the problem that medicine will always make you better.

 

[Drug Crazed]

So we don't assume it to be true for laughs and giggles we assume it to be true because there is no problem with the math that it uses?

Yes! That's just it! Though I have an urge to change math to maths. Don't mind me...

 

[castlewise]

Here

Ever heard of Proof By Induction?
First Step:
Assume true for n=1

Maths is all about assumption

Uh no in induction you have to prove n=1 is true. Then prove the general case 'n+1' is true (then you're done).

Off topic but fun anyway. All horses have the same color: A proof by induction.
Let n be the number of horses.

n=1: If there is only one horse then it has to be the same color as itself so we are good with this case.

Inductive step: Suppose all groups of horses with n animals have the same color. Suppose we have a group with n+1 animals. Take two of the animals, say Al and Betty. Remove animal Al from the group. The group has n horses so they all must have the same color. This means that Betty must have the same color as every other horse in the herd except Al and in particular the same color as some random third horse Carla. Now remove Betty and put Al back in. There are still n horses in the group so the horses all have the same color. So Al has the same color as Carla as well. Since Al has the same color as Carla, Al must have the same color as the rest of the herd (including Betty). So all n+1 animals have the same color.

By induction every horse is the same color.

(Note: this proof has a flaw, and its not the induction. So don't take it as some sort of demonstration that math/induction/proof is bs or whatever.)

 

[sarge1942]

my first thought was is it the right medicine, i don't like that question at all, insufficient data for me.
Edit: oh i just got what that meant, never mind the comment, except i still don't like the question.

 

[Sonic Doctor]

And it is useful, usely is not a word.

And I'm doing Computer Science with Maths and therefore am allowed to make typos.

I'm taking that as a joke, because that won't fly in college, even in writing things for Computer Science and Math classes. Besides, even if you are going into those fields when you get to college, you will still have to take at least two composition classes, a literature class or two, and a speech class. All of which will have a ton of writing, along with the ton of writing you will do with your Major course work. Just because you aren't going to be an English major, doesn't mean you won't have to write any papers and write very well.

If you are already in college, you already know this.

 

[Singletap]

Why make the truth table if it could be wrong. What if it ends up being true and it is actually false wouldn't that create a problem in a code?

It doesn't really matter if the medicine helps or not because this is just a thought exercise.

You could just as easily construct a truth table from any other premise. Perhaps it would be easier for you if I re-word it like this:

"It is the case that if you take your medicine then you will feel better."

It doesn't matter that the medicine may or may not work. You are being given a truth and being told to conclude from it using a truth table.

In the real world you'd determine the validity of the above statement using scientific tests. For your logic class, however, we can safely take it as a given because it's not being used to make any decisions beyond the classroom.

I understand you're getting worked up over the above statement because it's just as much an assumption to take it as a given that the medicine works as to take it that it doesn't. Let's pursue this, shall we?

Say that scientific trials confirm that the medicine works. The premise is valid.

Say that scientific trials confirm that the medicine does not work. The premise is invalid.

You are no longer working on an assumption. Or are you? You see, even those scientific trials operate on assumptions in maths and in the way we perceive the world. When it comes down to it, we can't really know anything other than the existence of our own consciousness. As Descartes said, "I think, therefore I am."

It is pointless, therefore, to get all worked up over this particular premise, and instead just accept that it's OK to take it as a truth for the purposes of the exercise. You're going to hit the wall of unknowable reality eventually as long as you apply your logic consistently.

So just accept it and enjoy the thought exercise.

Right everything could just be fake and it's assumed to be real. The point is it's useless to think like that or... okay... I may get it more now.

 

[Hawk of Battle]

1/3 + 1/3 +1/3 = 3/3 = 1

BUT

0.3 + 0.3 + 0.3 = 0.9

What happened to the 0.1?

Yeah, I'm gona go ahead and say maths is stupid.

 

[castlewise]

1/3 is not .3.
1/3 is .333333333... (repeating)

1/3+1/3+1/3 = .9999999999....

and there was already an escapsit thread about how .9999999...=1