Induction Query (1 Viewer)

[michaeljennings]

In an exam when you do induction and you try to prove the step n=k+1 will you get full marks if you prove it without using yoru assumption?

Sorry had to delete the question if you wanna see it pm me

 

[muzeikchun852]

In an exam when you do induction and you try to prove the step n=k+1 will you get full marks if you prove it without using yoru assumption?

hardly ever happen. you would mostly need your assumption to complete the prove in indication.

 

[michaeljennings]

hardly ever happen. you would mostly need your assumption to complete the prove in indication.

For a question today in our trial one of my mates prove that step without the assumption. Our teachers have never told us it is mandatory to use the assumption i was jsut curious

 

[muzeikchun852]

For a question today in our trial one of my mates prove that step without the assumption. Our teachers have never told us it is mandatory to use the assumption i was jsut curious

I don't know. you need to post the question or something to judge it accurately.

 

[michaeljennings]

its up

 

[Hermes1]

the assumption step is essential in any induction question. when u say ur teachers neva said its mandatory. wat do they recommend u do instead?

 

[michaeljennings]

the assumption step is essential in any induction question. when u say ur teachers neva said its mandatory. wat do they recommend u do instead?

Well to be honest i cant rememebr what exactly they said but from memory it was jsut as if the assumption aided the step where you had to prove n=k+1 but i wasnt sure if it was essential. I am hoping it is because a person i am currently beating by 0.07% proved it without using the assumption which i think is a little unfair on those who tried to do it properly but couldnt because his method only takes 5 mins but another one of my friends tried doing that question for 20 mins and in the end couldnt get it

 

[Hermes1]

Well to be honest i cant rememebr what exactly they said but from memory it was jsut as if the assumption aided the step where you had to prove n=k+1 but i wasnt sure if it was essential. I am hoping it is because a person i am currently beating by 0.07% proved it without using the assumption which i think is a little unfair on those who tried to do it properly but couldnt because his method only takes 5 mins but another one of my friends tried doing that question for 20 mins and in the end couldnt get it

well i dont no how ur teachers are going to mark it. but the induction process is very specific. and in the conclusion u actually mention that "having assumed true for n = k, it was proven true for n = k+1...", so this step has to be put in, unless that guy had some other way of holding his argument together.

 

[michaeljennings]

but technically he did prove for n=k+1 he jsut didnt use the assumption to prove it

 

[Hermes1]

but technically he did prove for n=k+1 he jsut didnt use the assumption to prove it

how can u do this.
with induction u r trying to prove a statement is true for a set of integers (e.g. n>0). now this is why the assumption is crucial. bcuz u assume for k and then prove for k+1. this allows u to say that the statement is true for all n (n>0).

did he say what he put in instead of the assumption?

 

[Hermes1]

http://www.themathpage.com/aprecalc/mathematical-induction.htm

read this

 

[muzeikchun852]

but technically he did prove for n=k+1 he jsut didnt use the assumption to prove it

that question you posted had a problem itself. you can simply prove it normally without induction. but if your teacher designed this question to test induction specifically, no, I personally dont think your enemy will get the mark for it.

 

[muzeikchun852]

how can u do this.
with induction u r trying to prove a statement is true for a set of integers (e.g. n>0). now this is why the assumption is crucial. bcuz u assume for k and then prove for k+1. this allows u to say that the statement is true for all n (n>0).

did he say what he put in instead of the assumption?

it is a combination prove. so you can do it without induction.

 

[michaeljennings]

how can u do this.
with induction u r trying to prove a statement is true for a set of integers (e.g. n>0). now this is why the assumption is crucial. bcuz u assume for k and then prove for k+1. this allows u to say that the statement is true for all n (n>0).

did he say what he put in instead of the assumption?

okay so you had to prove for n=k+1 yeah? you have the original queston i had to delete it for safety reasons cos someone was away today i dont wanan get busted. if you sub in k+1 to the left hand side and just put it over a common denominator it equals to the RHS when you simplify it and you dont need the assumption at all but to me thats unfair cos doing it that way literally takes 1 minute..

 

[Hermes1]

okay so you had to prove for n=k+1 yeah? you have the original queston i had to delete it for safety reasons cos someone was away today i dont wanan get busted. if you sub in k+1 to the left hand side and just put it over a common denominator it equals to the RHS when you simplify it and you dont need the assumption at all but to me thats unfair cos doing it that way literally takes 1 minute..

but thats not actually proving via induction. thats just saying it works for one integer k+1. his method is not actually showing it works for the integers before and after it. but if you assume for n = k and prove for n = k+1 u actually prove it works for successive integers and you can say that it works for all positive integers etc.
i highly doubt a school like Baulkham hills would allow his method to be given full marks bcuz its not actually correct.

 

[Hermes1]

also dont u hav ur physics trial tomorrow. go 2 sleep lol.

 

[michaeljennings]

but thats not actually proving via induction. thats just saying it works for one integer k+1. his method is not actually showing it works for the integers before and after it. but if you assume for n = k and prove for n = k+1 u actually prove it works for successive integers and you can say that it works for all positive integers etc.
i highly doubt a school like Baulkham hills would allow his method to be given full marks bcuz its not actually correct.

yeahh thats what i was thinking but the guy who did it asked his tutor and his tutor said it was fine...personally i dont think its answering the question as it did say prove by Mathematical indcution. It was worht 4 marks you rkn they will give him 2 or 3?

 

[michaeljennings]

also dont u hav ur physics trial tomorrow. go 2 sleep lol.

yeah lol still learning about motors and generators hahahahah

 

[Hermes1]

yeahh thats what i was thinking but the guy who did it asked his tutor and his tutor said it was fine...personally i dont think its answering the question as it did say prove by Mathematical indcution. It was worht 4 marks you rkn they will give him 2 or 3?

he defs shouldnt get 4. if he gets lucky they could give him 3. but most probably 2. lol the only reason MI questions are 4 marks is bcuz of the specific method u hav to go through markers are not goin to be happy if u r takin shortcuts.

 

[michaeljennings]

he defs shouldnt get 4. if he gets lucky they could give him 3. but most probably 2. lol the only reason MI questions are 4 marks is bcuz of the specific method u hav to go through markers are not goin to be happy if u r takin shortcuts.

hahah yes this is good then cos so far ive lsot 2 marks, and he has lsot the exact same 2 plus this induction question so hopefully i beat him. He rkns we are both in the top 10 but i think we are just outside of it but i cant be sure lol. I would be over the moon if i finished in the top 5