Format for Mathematical Induction proofs <3 (1 Viewer)

[SadCeliac]

Hi all,

Just clarifying if this is the correct way to set out induction proofs (this is how I've done it all through high school):

(A) Consider n = 1:
prove base case

(B) Assume true for n = k:
rewrite given statement for k instead of n

Consider n = k + 1:
ie. RTP <what I need to prove with n = k + 1>

proof --insert assumption somewhere obviously

Conclusion: therefore by (A), (B), and the process of Mathematical Induction, TRUE

Is this fine??

THANKS

 

[carrotsss]

Yes that’s perfectly fine. Personally the way I was taught to do it is this (my teacher based it off some NESA materials so it should be fine):

Step 1 Show true for n=1
LHS=thing RHS=thing
.: True for n=1
Step 2 Assume true for n=k
i.e. LHS with k=RHS with k
Step 3 Prove true for n=k+1
RTP -> LHS with k+1=RHS with k+1
LHS=…
=…
=RHS
.: True for n=k+1
Hence the statement is true for all positive integers n>=1, by induction

 

[Drongoski]

Don't forget, sometimes, the base case maybe for, say, n = 3 instead of 1.

 

[SadCeliac]

Don't forget, sometimes, the base case maybe for, say, n = 3 instead of 1.

yeah lol I didn't really want to include that in my first post bc im lazy

also like it may not be n = k+1 e.g. for even or odd numbers etc etc

 

[SadCeliac]

Yes that’s perfectly fine. Personally the way I was taught to do it is this (my teacher based it off some NESA materials so it should be fine):

Step 1 Show true for n=1
LHS=thing RHS=thing
.: True for n=1
Step 2 Assume true for n=k
i.e. LHS with k=RHS with k
Step 3 Prove true for n=k+1
RTP -> LHS with k+1=RHS with k+1
LHS=…
=…
=RHS
.: True for n=k+1
Hence the statement is true for all positive integers n>=1, by induction

thanks 🥕 <333

edit: how cool I made the emoji for a carrot your user tag, because your name is carrots WOAH INSANE
bruh im living in my own world someone help

 

[scaryshark09]

Don't forget, sometimes, the base case maybe for, say, n = 3 instead of 1.

yeah true for ext 2
ext 1 they can only ask n>=1 (or just positive integer which means the same thing) it says somewhere in the syllubus

 

[scaryshark09]

our trial they were stupid and did 0 tho cause they are used to old syllabus.
but new syllabus is only n>=1 for ext 1

ext 2 they can throw anything at you

 

[synthesisFR]

thanks 🥕 <333

edit: how cool I made the emoji for a carrot your user tag, because your name is carrots WOAH INSANE
bruh im living in my own world someone help

did u tear up or cry in graduation yesterday?
this is not looking good i was watching a past graduation ceremony from my school and i was literally tearing up at that. im actually gonna cry in graduation especially when they play that graduation video with the sad but uplifting music this is not looking good

 

[synthesisFR]

my eco teacher was saying today how the saddest part is when everyone starts walking out of the school and leaving after the ceremony and it starts to get empty thats when it really hits u

 

[SadCeliac]

did u tear up or cry in graduation yesterday?
this is not looking good i was watching a past graduation ceremony from my school and i was literally tearing up at that. im actually gonna cry in graduation especially when they play that graduation video with the sad but uplifting music this is not looking good

personally I'm not a big crier, I'm just really happy with what I've achieved in high school, got myself a few awards, really happy with all the friendships I've made
I don't think there's a point being sad, rather just being happy that everything good happened

so no I didn't cry at my ceremony last night

@synthesisFR which school's ceremony did you watch / how did you get the stream

also when are you graduating, when's your ceremony

 

[SadCeliac]

my eco teacher was saying today how the saddest part is when everyone starts walking out of the school and leaving after the ceremony and it starts to get empty thats when it really hits u

yeah look my friends and I just hung out in the auditorium for the last time after the ceremony and took a bunch of photos, everyone was gone and it was just us I agree it was sad then

 

[synthesisFR]

personally I'm not a big crier, I'm just really happy with what I've achieved in high school, got myself a few awards, really happy with all the friendships I've made
I don't think there's a point being sad, rather just being happy that everything good happened

so no I didn't cry at my ceremony last night

@synthesisFR which school's ceremony did you watch / how did you get the stream

also when are you graduating, when's your ceremony

1- Nah same but except im being more pessimistic and feels sad bc the good times iv'e had are ending. Plus i really really hate changes in my life thats just me i don't like big changes.
2- My schools past ceremony so i just watched that for a bit
3- can't tell to not get doxxed potentially just in case

 

[its_ace21]

did u tear up or cry in graduation yesterday?
this is not looking good i was watching a past graduation ceremony from my school and i was literally tearing up at that. im actually gonna cry in graduation especially when they play that graduation video with the sad but uplifting music this is not looking good

i was about to start crying when the year 12's last year graduated idk what im gonna do on my graduation

 

[SadCeliac]

i was about to start crying when the year 12's last year graduated idk what im gonna do on my graduation

stand on stage for a minute while your mentor tells you about all the things you did in high school because they do that for everyone and the ceremony goes for five hours but its actually really sweet and cute and ugh i miss school

 

[its_ace21]

stand on stage for a minute while your mentor tells you about all the things you did in high school because they do that for everyone and the ceremony goes for five hours but its actually really sweet and cute and ugh i miss school

stop i actually miss school fueirbgie my grads in november

 

[ExtremelyBoredUser]

Just use whatever method your school makes you do since it'll flow naturally for you in the HSC. There shouldn't be too much issues given you get the general gist of induction (base e.g P(1), assumption step e.g P(k), P(k+1) step, acknowledge how P(k) -> P(k+1) makes statement true) since markers understand everyone does their wording/phrasing differently.

 

[Average Boreduser]

Hi all,

Just clarifying if this is the correct way to set out induction proofs (this is how I've done it all through high school):

(A) Consider n = 1:
prove base case

(B) Assume true for n = k:
rewrite given statement for k instead of n

Consider n = k + 1:
ie. RTP <what I need to prove with n = k + 1>

proof --insert assumption somewhere obviously

Conclusion: therefore by (A), (B), and the process of Mathematical Induction, TRUE

Is this fine??

THANKS

For step three, I was taught to go further indepth in the reasoning. I heard in the HSC they're really stingy with the format of induction qns
e.g S3): It is true for n=1 (S1)
therefore, it is true for n= 1+1=2, 1+2=3, ...
So it is true for all integers n>=1


Take this with a grain of salt though, as I don't think its too significant.
- Hope this helps!

 

[carrotsss]

For step three, I was taught to go further indepth in the reasoning. I heard in the HSC they're really stingy with the format of induction qns
e.g S3): It is true for n=1 (S1)
therefore, it is true for n= 1+1=2, 1+2=3, ...
So it is true for all integers n>=1


Take this with a grain of salt though, as I don't think its too significant.
- Hope this helps!

I can’t seem to find it but my teacher showed us some hsc marking centre notes which explicitly said that that was unnecessary, and said that something like “hence the statement is true for all n>=1 by induction” is sufficient, and hsc sample answers use a similar statement

 

[SadCeliac]

I can’t seem to find it but my teacher showed us some hsc marking centre notes which explicitly said that that was unnecessary, and said that something like “hence the statement is true for all n>=1 by induction” is sufficient, and hsc sample answers use a similar statement

tbh I do the last statement out of a courtesy to the marker to let them know my proof is done lol