A-Level Maths: A1-04 [Introducing Proof by Exhaustion]

[c.l.]

"So proof by exhaustion sounds like it's going to be tiring work, mkay?" gotta rate those dad jokes guys. Top notch.

[alannatomlinson]

this is AMAZING esp when i want to get a head start on revision during Corona

[sewind]

Wow. This playlist is a goldmine, beyond amazing. Thank you so much.

[thatonerandom]

Liked the unintentional Pun at the start of the video

[radheypatel]

An alternative way to think about how many numbers you must test for divisibility is to work out the closest number greater than the conjecture that is a square number, and test divisibility up to the square root of that square number. For example, in this case, 100 is the closest square number to 97, hence you only need to test for divisibility until 10. Another example is 119, and as 121 is the closest square number to 119, you only need to test up to 11.
Of course, as you divide by 2 and 3, you already know the outcome for 6, etc. But when dealing with larger and more complex questions (which, yes, is unlikely at A-Level), you eliminate unnecessary calculations alongside having an accurate understanding of when to stop dividing.
Hope this helps!
P.S. Do let me know if there are examples where this would not work.

[loggingoff]

im 16 just got an 8 in gcse maths and these videos are really helpful as im starting alevel maths, thank u

[raiturner]

Finally maths is made easy to understand

[ht-vefe]

only teacher I know who deserves more pay

[bigbobey]

You explain very very well. Thank you.

[Doodo]

So root 97 is 9.8.., for example let say the a square root of a number is 10.2 would I still divide by 10?

[mihirdutta-DPSi]

Outstanding.
If the narrative at 7:00 is watched first, the reasoning might be more understandable to young learners.

[docgraal]

Can you explain why if a number is not a factor of a number then a larger number is "certainly" not a factor such as 2 and 6 or 2 and 4

[Awai_quotes]

Hey i dont understand the last part how you got the value n=3k, n=3k-1,n=3k-2 (if its says i more than the multiple of 9 then why we subtracting-2

[akidanis]

Couldn't we just prove by doing LCM though? That would be quicker don't you think? If you can't use it, can you say why?

[shahendra]

aren't 1 and 97 still factors so there would technically be a factor below root97 and above root97? Would you need to mention something like 'As there are no factors other than 1 < sqrt(97)' or would it not matter if you were to write this in an exam question

[bryannaedjah-opata]

Hi there, you explained that if there are no factors below the square root of the number then it implies that it is a prime number but what about the numbers that have only four factors being two primes, 1 and itself, for example 91. The square root of 91 is probably around 9.5 but 13 is above 9.5 so how would this method be guaranteed?

[aidenstonehouse]

Can someone explain why if it is not divisible by 2 it is not divisible by 4, the same for 3 and 6...

[methuzla]

Not sure that decimals belong with Proof by Exhaustion (otherwise ennumeration), old and new worlds.

I t would be better to say
97 = 2 × 48 remainder 1
= 3 × 32 remainder 1
= 4 × 24 remainder 1 (already dealt with by case 2)
= 5 × 19 remainder 2
etc
up to factorisation by 10 where 10 × 10 is the first square larger than 97
(although since 10 = 5 × 2, that is already dealt with)