Questions involving LHS=RHS (2 Viewers)

[robjoker]

Hi!
I've been recently doing the topic of mathematical induction and have come across questions where you have to prove LHS=RHS (especially in the 'PROVE: n=k+1' step)
I was just wondering if marks would be deducted if i wrote:

LHS=...=...= x
RHS=...=...= x
Thus, LHS=RHS

Instead of:

LHS=...=...=...=RHS

THANKS!

 

[deswa1]

Depends on the marker. Its right but I know a few teachers that frown on that sort of thing even though there's nothing wrong with it. I'm guessing you can so it in the HSC but maybe someone else can confirm. Honestly though, if you've proven that LHS=x=RHS, just reverse the steps you used to get from RHS to x and then you can go directly from LHS to RHS which is neater.

 

[king chopper]

Its completely fine

 

[Carrotsticks]

In the HSC, no.

In your school exams perhaps, as schools can mark differently to HSC (ridiculous imo)

However if they deducted you for that, try to fight for your precious marks.

 

[4025808]

IMO that up there is a valid proof, as you aren't assuming that either side is true. So I seriously wouldn't understand why teachers would deduct marks for proving LHS, getting to a certain point, and then RHS.

 

[Carrotsticks]

IMO that up there is a valid proof, as you aren't assuming that either side is true. So I seriously wouldn't understand why teachers would deduct marks for proving LHS, getting to a certain point, and then RHS.

Many teachers do not allow 'faster' methods because they believe that the shorter way (even if Mathematically correct) is less 'correct' than the longer way.

You would be surprised.

 

[cormacshaw]

That's just it though, OP is doing the longer way of showing LHS, then doing RHS, and then showing that both are correct, instead of the second method. Heck, even my textbook uses the first way.

Weird.

 

[4025808]

Many teachers do not allow 'faster' methods because they believe that the shorter way (even if Mathematically correct) is less 'correct' than the longer way.

You would be surprised.

I remember the time when I was looking at SpiralFlex's solutions to simplifying a trigonometric equation, the Maths head teacher gave no marks simply because he multiplied top and bottom to make thing's easier. I personally believed that it was a smart way out and would have given him full marks for it.

2400th post.

 

[Carrotsticks]

I remember the time when I was looking at SpiralFlex's solutions to simplifying a trigonometric equation, the Maths head teacher gave no marks simply because he multiplied top and bottom to make thing's easier. I personally believed that it was a smart way out and would have given him full marks for it.

It's almost as if they wish to suppress elegance of solutions, and promoting brute force methods of Mathematics.

 

[Ferox]

a=c
b=c
therefore a=b for all real a,b,c

That's perfect logic. I'd have a fit if a teacher marked that wrong.

 

[Carrotsticks]

a=c
b=c
therefore a=b for all real a,b,c

That's perfect logic. I'd have a fit if a teacher marked that wrong.

Let a cat = C

Let a dog = D

Let 4 legs = L

C = L since cats have 4 legs.

D = L since dots have 4 legs too.

Therefore, C = D.

 

[Ferox]

My Analysis isn't great but I think you've misused the equality sign there.

cat = C
dog = D
4 legs = L
:. C ∈ L
and D ∈ L

That doesn't meant C=D


What I've written in post 10 is, from memory, the transitive property of equality, and is true.
EDIT: Write that next to your proof if you're uncertain.

 

[Carrotsticks]

My Analysis isn't great but I think you've misused the equality sign there.

cat = C
dog = D
4 legs = L
C ∈ L
D ∈ L

That doesn't meant C=D


What I've written in my above post is, from memory, the transitive property of equality, and is true.
EDIT: Write that next to your proof if you're uncertain.

I am aware of this, I was simply making a point regarding your "I'd have a fit if a teacher marked it wrong"

Way to ruin it haha, I was waiting for some "Hey, this seems legit... why doesn't it work?".

 

[Ferox]

ha, well you got me. I still can't believe any teacher would have a problem with that.

 

[Drongoski]

Hi!
I've been recently doing the topic of mathematical induction and have come across questions where you have to prove LHS=RHS (especially in the 'PROVE: n=k+1' step)
I was just wondering if marks would be deducted if i wrote:

LHS=...=...= x
RHS=...=...= x
Thus, LHS=RHS

Instead of:

LHS=...=...=...=RHS

THANKS!

Should be fine. Teachers marking this "wrong" are wrong.

 

[Nooblet94]

Many teachers do not allow 'faster' methods because they believe that the shorter way (even if Mathematically correct) is less 'correct' than the longer way.

You would be surprised.

This. I lost a mark for using parametric differentiation in a test last year, rather than converting the parametric equation to cartesian and differentiating. Teacher even said it was correct but refused to give me the mark because it wasn't "as correct".

More importantly, I don't see why you'd want to do it that way unless you were really stuck or something, it's only going to take longer IMO. That being said, it's still perfectly correct.

 

[Carrotsticks]

Was it a test that counted to Year 12 HSC? Were you the only one who got deducted for using parametric differentiation?

 

[deswa1]

This. I lost a mark for using parametric differentiation in a test last year, rather than converting the parametric equation to cartesian and differentiating. Teacher even said it was correct but refused to give me the mark because it wasn't "as correct".

More importantly, I don't see why you'd want to do it that way unless you were really stuck or something, it's only going to take longer IMO. That being said, it's still perfectly correct.

Wait what? Did you argue like hell for that?

 

[kkmok]

sometimes maths teacher is just ridiculous, when I was doing 4unit trial exam, I got 4 marks deduct because the teacher don't understand my proof.
I did something similar, i said 2 - 1/k + 1/(k+1)^2 < 2 - 1/(k+1) in the induction
with further explanation why this work. another few lines of working out to prove 1/k - 1/(k+1)^2 > 1/(k+1)

just like using lemma and axiom to prove other stuff>.>
lucky i still got rank 1 for my internal(school) rank lol

 

[robjoker]

Thanks everyone for the responses!
I asked my maths teacher and he said that it usually depends on the marker. He said that it was a good idea to just go from LHS=RHS but if this was too hard to figure out then i should just do the RHS=x part on a scrap piece of paper and then work from x to RHS in my answer.
Again, thanks!