Conclusion for Induction (2 Viewers)

[SpiralFlex]

I write "hence true for all integers n>= (the restriction)"

You don't get any marks for it lol

Why not

 

[tywebb]

Suppose it were a strong induction question.

Would you get a mark for the basis step?

Or full marks for ONLY the strong induction step (understanding the superfluity of the basis step)?

Or BONUS marks for explaining the superfluity of the basis step?

 

[Frie]

Suppose it were a strong induction question.

Would you get a mark for the basis step?

Or full marks for ONLY the strong induction step (understanding the superfluity of the basis step)?

Or BONUS marks for explaining the superfluity of the basis step?

What is a basis step?

The way i learnt it was in 3 steps

Prove it works for n = 1 (or otherwise lowest possible integer)
Then do n = k
And then do n = k + 1 (unless otherwise asked)

 

[tywebb]

You are describing ordinary induction, not strong induction.

 

[RealiseNothing]

No such think as a bonus mark, you'll never (probably) get 4/3

And usually you don't get marks for "show true for n=1" (or first non-restriction) because any idiot could do that, likewise for "assume true for n=k" but I would guess if it is like a really "strong induction" and it is later in the paper, as the markers feel sorry for you, then you could get 1 mark. Other then that, the marks come from the algebra in step 3 using the assumption

No, you get 1 mark for proving true for n=1 and 2 marks for the algebra part of proving true for n=k+1.

 

[tywebb]

I don't think you guys really know about strong induction.

It's to assume S(1), S(2) ... S(k) are true in order to prove S(k + 1) is true.

If you can do that then there is no need to prove S(1). However most would still do that anyway. Just to feel safe. In case a mark IS awarded for it. Even though it is not needed!

Here is a more thorough discussion about the superfluity of the basis step in a strong induction (and transfinite induction):

http://mathoverflow.net/questions/11964/strong-induction-without-a-base-case

 

[CM07]

I just write "hence proven by mathematical induction".

What the hell is strong induction oh my god.

 

[SpiralFlex]

I don't think it is too (something like this would surely be left for 4U). There are other variants to mathematical induction, you guys only learn the first principle of mathematical induction.

 

[RealiseNothing]

I don't think this so called "strong induction" is in the 3U course

Yer this, it's only in 4U.

 

[tywebb]

Yeah. But there is a very subtle reason why I'm posing this question in this thread.

No mark will be awarded for a conclusion - because it is not needed. In fact many proofs by induction in research papers omit a conclusion for this very same reason.

But if it were a strong induction question, a mark will almost certainly be awarded for the basis step - despite the fact that it is not needed.

This is clearly a contradiction. ... One that needs to be discussed. ... In this thread.

 

[Trebla]

See the marking criteria for Q12a) of last year's HSC: http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2012exams/pdf_doc/maths-ext-1-marking-guide-12.pdf

Question 12 (a)
• Correct proof - 3 marks
• Attempts to do the induction step - 2 marks
• Proves case for n = 1, or equivalent merit - 1 mark

 

[RealiseNothing]

That can't be right. 1 mark for subbing in a number in the harder part of the paper?

See the marking criteria for Q12a) of last year's HSC: http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2012exams/pdf_doc/maths-ext-1-marking-guide-12.pdf

Question 12 (a)
• Correct proof - 3 marks
• Attempts to do the induction step - 2 marks
• Proves case for n = 1, or equivalent merit - 1 mark

.

 

[BlugyBlug]

Why not

Because otherwise if you couldn't do the question all you have to write is "hence true by mathematical induction" and still get 1 mark by doing nothing.