0=2, math inside.

[Nivag the Owl]

Mathematics as an expression isn't always 100% perfect and you can occasionally stumble on the "proof" for ridiculous claims like this. I remember reading some one 1 = 2. I remember it said a good way to disprove it is to actually apply it to a physical experiment.

No. If you stumble on that sort of proof, then you've made an error in your calculations. Check for divisions by zero, not being careful with square roots, etc. The only time when maths breaks down is if you're trying to apply a model to describe a physical experiment (because there will always be factors the model will ignore). If you're trying to do something strictly with numbers, without using experimental data at all, and you get a result telling you 1 = 2, then you've made a mistake.

Maths is perfect. We haven't discovered everything we need to know, but never be so arrogant as to blame mathematics for being inconsistant. It's not maths that's wrong, it's YOUR maths that are wrong. It's when you apply the maths to real things when you get errors. Look at trying to predict the weather, for example.

Dude calm down. I'm not being arrogant. I'm sharing something I've fucking READ, ok? I'm not just jumping into a thread to say maths is shit and doesn't mean anything. In fact, my post (as un-spell-checked as it may be) is agreeing that these claims are incorrect and can be disproved.

 

[benylor]

I'm sorry what do you define as rel maths degrees are perfectly fine. Also if he is using degrees or radians this should have already been stated or it is assumed degrees are used.

Degrees don't work if you start doing calculus, you need radians for that. If you see a cos pi anywhere, then it's almost certainly in radians. And, finally, at university level you just assume that you're using radians. Degrees are just a simplification that's easier for lay people to understand. I wouldn't like to teach a child to read angles in radians right off the bat.

Degrees just don't get used at all once you reach university.

 

[Rakkana]

I most definitively understood every single word of that...

 

[Glademaster_v1legacy]

I'm sorry what do you define as rel maths degrees are perfectly fine. Also if he is using degrees or radians this should have already been stated or it is assumed degrees are used.

Degrees don't work if you start doing calculus, you need radians for that. If you see a cos pi anywhere, then it's almost certainly in radians. And, finally, at university level you just assume that you're using radians. Degrees are just a simplification that's easier for lay people to understand. I wouldn't like to teach a child to read angles in radians right off the bat.

Degrees just don't get used at all once you reach university.

Yes while I understand that Calculus is only one branch of maths and the fact should of still been stated before the "proof" was given. While I also understand that degrees are a simplicated for people to understand it is still common currency for people to use. Unless your in Calculus class/have it stated most people myself included will assume you are using degrees. Regardless of what cos pi is usually used in.

 

[Showsni]

Of course, you can prove that 0=2 in, say, modulo 2 arithmetic...

1 + 1 (mod 2) = 0

Therefore, 2 = 0

That's pretty obvious and unhelpful, though.

 

[SnipErlite]

cos[sup]2[/sup]x=1-sin[sup]2[/sup]x
cos x = (1-sin[sup]2[/sup]x)[sup]1/2[/sup]

cos[sup]2[/sup]x does not equal (cos x)[sup]2[/sup] and therefore cannot be rooted

 

[benylor]

Mathematics as an expression isn't always 100% perfect and you can occasionally stumble on the "proof" for ridiculous claims like this. I remember reading some one 1 = 2. I remember it said a good way to disprove it is to actually apply it to a physical experiment.

No. If you stumble on that sort of proof, then you've made an error in your calculations. Check for divisions by zero, not being careful with square roots, etc. The only time when maths breaks down is if you're trying to apply a model to describe a physical experiment (because there will always be factors the model will ignore). If you're trying to do something strictly with numbers, without using experimental data at all, and you get a result telling you 1 = 2, then you've made a mistake.

Maths is perfect. We haven't discovered everything we need to know, but never be so arrogant as to blame mathematics for being inconsistant. It's not maths that's wrong, it's YOUR maths that are wrong. It's when you apply the maths to real things when you get errors. Look at trying to predict the weather, for example.

Dude calm down. I'm not being arrogant. I'm sharing something I've fucking READ, ok? I'm not just jumping into a thread to say maths is shit and doesn't mean anything. In fact, my post (as un-spell-checked as it may be) is agreeing that these claims are incorrect and can be disproved.

Okay, I apologise. Your first line was a little unclear, which led to me misinterpreting the whole post. My point stands, but in agreement to you instead of against you.

Sometimes it feels like every poster in a thread is the same guy, so I tend to get frustrated a little too quickly. Sorry about that.

 

[Nivag the Owl]

Mathematics as an expression isn't always 100% perfect and you can occasionally stumble on the "proof" for ridiculous claims like this. I remember reading some one 1 = 2. I remember it said a good way to disprove it is to actually apply it to a physical experiment.

No. If you stumble on that sort of proof, then you've made an error in your calculations. Check for divisions by zero, not being careful with square roots, etc. The only time when maths breaks down is if you're trying to apply a model to describe a physical experiment (because there will always be factors the model will ignore). If you're trying to do something strictly with numbers, without using experimental data at all, and you get a result telling you 1 = 2, then you've made a mistake.

Maths is perfect. We haven't discovered everything we need to know, but never be so arrogant as to blame mathematics for being inconsistant. It's not maths that's wrong, it's YOUR maths that are wrong. It's when you apply the maths to real things when you get errors. Look at trying to predict the weather, for example.

Dude calm down. I'm not being arrogant. I'm sharing something I've fucking READ, ok? I'm not just jumping into a thread to say maths is shit and doesn't mean anything. In fact, my post (as un-spell-checked as it may be) is agreeing that these claims are incorrect and can be disproved.

Okay, I apologise. Your first line was a little unclear, which led to me misinterpreting the whole post. My point stands, but in agreement to you instead of against you.

Sometimes it feels like every poster in a thread is the same guy, so I tend to get frustrated a little too quickly. Sorry about that.

No problem. We're cool.

 

[benylor]

I'm sorry what do you define as rel maths degrees are perfectly fine. Also if he is using degrees or radians this should have already been stated or it is assumed degrees are used.

Degrees don't work if you start doing calculus, you need radians for that. If you see a cos pi anywhere, then it's almost certainly in radians. And, finally, at university level you just assume that you're using radians. Degrees are just a simplification that's easier for lay people to understand. I wouldn't like to teach a child to read angles in radians right off the bat.

Degrees just don't get used at all once you reach university.

Yes while I understand that Calculus is only one branch of maths and the fact should of still been stated before the "proof" was given. While I also understand that degrees are a simplicated for people to understand it is still common currency for people to use. Unless your in Calculus class/have it stated most people myself included will assume you are using degrees. Regardless of what cos pi is usually used in.

I guess more caution should be used with regards to assumptions on the internet. Still, when is anybody using degrees going to start talking about cos(pi)?

SNIP
But it isn't sin^2 or cos^2 as cos^2 has been canceled while sin^2 remains so we are left with a sin^2 and a cos so cos pi is not 1.

You misunderstand, sir.

The first equation in the problem is cos^2(x) = 1-sin^2(x). This is true for ANY x. You can pick any value of x you like for that equation, and it will still be true - it's more than an equation, it's an identity.

So, the flaw in the maths can not be that he has pulled the value of x out of his arse, as you have said. The first line is true for any x.

If you really want to go down that root then you can write square root of 2 as a fraction and get 2=1. While it may be true what he was done when he used X as number(pi) is not true as he has not stated that he is using radians so the general world will assume he is using degree even taking that into account. As you said the flaw is also a square root could be the number+ or -.

Okay, you lost me there. I think we might be arguing about something that doesn't have anything to do with what I thought we were arguing about.

Is this about what unit he's using? Because that is relevant here, an error only forms in that post if cos (x) and sin (x) having the same sign does not correspond properly with which square root you use.

Trigonometric function of pi always means radians, though >_>

 

[JourneyThroughHell]

EDIT2: Alright, I asked my calc professor, and he went about saying that I didn't restrict the domain, thus allowed square root problem.

Fairly obvious.
Friendly advice, you really need to "restrict your domain" (I don't know how to say D in English) as often as you can.

 

[Doug]

Agreed. You can't square root both sides of an equation. You could divide both sins of the equation by cos x, and get cos x = (1 - sin[sup]2[/sup] x) / cos x

At x = pi,
-1 = (1 - 0) / -1
-1 = -1

Yes you can, otherwise a lot of maths we base technology on would be instantly wrong

Square route both sides of an equation? What technology uses that then?

And no, you can't, because its the same as saying...

x[sup]2[/sup] = y[sup]2[/sup] implies that

x[sup]2[/sup]/x == y[sup]2[/sup]/y

If we say x = -2, and y = 2, that doesn't work; i.e. 4/-2 = 4/2, which is wrong.

x[sup]2[/sup]/x == y[sup]2[/sup]/x works however; i.e. 4/-2 = 4/-2

 

[benylor]

Agreed. You can't square root both sides of an equation. You could divide both sins of the equation by cos x, and get cos x = (1 - sin[sup]2[/sup] x) / cos x

At x = pi,
-1 = (1 - 0) / -1
-1 = -1

Yes you can, otherwise a lot of maths we base technology on would be instantly wrong

Square route both sides of an equation? What technology uses that then?

And no, you can't, because its the same as saying...

x[sup]2[/sup] = y[sup]2[/sup] implies that

x[sup]2[/sup]/x == y[sup]2[/sup]/y

If we say x = -2, and y = 2, that doesn't work; i.e. 4/-2 = 4/2, which is wrong.

x[sup]2[/sup]/x == y[sup]2[/sup]/x works however; i.e. 4/-2 = 4/-2

You can, however, do it if you restrict the domain.

For x >= 0, y >= 0,
x^2 = y^2
x = y.

So it only doesn't work if x and y have different signs, in which case you have to stick a minus in front of one of them.

I'm not sure whether I'm agreeing with you or disagreeing with you here btw. Can't tell exactly what you're trying to say, but I suspect that what I say might actually be in agreement with you.

 

[PinkAngelKitty]

The error is that it's a fallacy. :/

 

[Kazturkey]

Agreed. You can't square root both sides of an equation. You could divide both sins of the equation by cos x, and get cos x = (1 - sin[sup]2[/sup] x) / cos x

At x = pi,
-1 = (1 - 0) / -1
-1 = -1

Yes you can, otherwise a lot of maths we base technology on would be instantly wrong

Square route both sides of an equation? What technology uses that then?

And no, you can't, because its the same as saying...

x[sup]2[/sup] = y[sup]2[/sup] implies that

x[sup]2[/sup]/x == y[sup]2[/sup]/y

If we say x = -2, and y = 2, that doesn't work; i.e. 4/-2 = 4/2, which is wrong.

x[sup]2[/sup]/x == y[sup]2[/sup]/x works however; i.e. 4/-2 = 4/-2

Pretty much this. -2 squared equals 2 squared, but 2 does not equal -2.

 

[Eat Uranium]

cos[sup]2[/sup]x=1-sin[sup]2[/sup]x
cos x = (1-sin[sup]2[/sup]x)[sup]1/2[/sup]

cos[sup]2[/sup]x does not equal (cos x)[sup]2[/sup] and therefore cannot be rooted

Well what does it equal then?

As far as I'm aware, cos[sup]2[/sup] (x) = (cos (x))[sup]2[/sup]

 

[Glademaster_v1legacy]

I'm sorry what do you define as rel maths degrees are perfectly fine. Also if he is using degrees or radians this should have already been stated or it is assumed degrees are used.

Degrees don't work if you start doing calculus, you need radians for that. If you see a cos pi anywhere, then it's almost certainly in radians. And, finally, at university level you just assume that you're using radians. Degrees are just a simplification that's easier for lay people to understand. I wouldn't like to teach a child to read angles in radians right off the bat.

Degrees just don't get used at all once you reach university.

Yes while I understand that Calculus is only one branch of maths and the fact should of still been stated before the "proof" was given. While I also understand that degrees are a simplicated for people to understand it is still common currency for people to use. Unless your in Calculus class/have it stated most people myself included will assume you are using degrees. Regardless of what cos pi is usually used in.

I guess more caution should be used with regards to assumptions on the internet. Still, when is anybody using degrees going to start talking about cos(pi)?

SNIP
But it isn't sin^2 or cos^2 as cos^2 has been canceled while sin^2 remains so we are left with a sin^2 and a cos so cos pi is not 1.

You misunderstand, sir.

The first equation in the problem is cos^2(x) = 1-sin^2(x). This is true for ANY x. You can pick any value of x you like for that equation, and it will still be true - it's more than an equation, it's an identity.

So, the flaw in the maths can not be that he has pulled the value of x out of his arse, as you have said. The first line is true for any x.

If you really want to go down that root then you can write square root of 2 as a fraction and get 2=1. While it may be true what he was done when he used X as number(pi) is not true as he has not stated that he is using radians so the general world will assume he is using degree even taking that into account. As you said the flaw is also a square root could be the number+ or -.

Okay, you lost me there. I think we might be arguing about something that doesn't have anything to do with what I thought we were arguing about.

Is this about what unit he's using? Because that is relevant here, an error only forms in that post if cos (x) and sin (x) having the same sign does not correspond properly with which square root you use.

Trigonometric function of pi always means radians, though >_>

I dunno I think we've gone a bit off topic I don't even know anymore.

 

[shroomz]

The Snip

for example,
evaluate x:

(3x+5)^2=81
my bad with the technology, i was trying to point out that raising both sides of an equation to a power is often required to solve it, but kinda shot myself in the foot there

 

[SnipErlite]

cos[sup]2[/sup]x=1-sin[sup]2[/sup]x
cos x = (1-sin[sup]2[/sup]x)[sup]1/2[/sup]

cos[sup]2[/sup]x does not equal (cos x)[sup]2[/sup] and therefore cannot be rooted

Well what does it equal then?

As far as I'm aware, cos[sup]2[/sup] (x) = (cos (x))[sup]2[/sup]

*Face whitens with horror* ooooh my bad, sorry you are correct, I'm an idiot and am surprised I made such an error.
Yes cos[sup]2[/sup] (x) = (cos (x))[sup]2[/sup].

Seriously I must've been well tired when I typed that.

[sub] I'm a mathematician/physicist. How did I make that bad an error?![/sub]