Methods of Proof | A-level Mathematics
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- čas přidán 3. 02. 2021
- The four main types of proof you need to be familiar with in A-level mathematics:
- proof by deduction
- proof by exhaustion
- proof by counter-example
- proof by contradiction
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100 greatest theorems of all time - pirate.shu.edu/~kahlnath/Top10...
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This is the simplest and understandable explaination for methods of proof which I found on you tube with such relevant examples. I was able to understand the concept in just one go. Feeling greatful to find this channel. Thank you so much 🥰🥰
bro fr saved my life with the easiest most simplest explanation of proofs. tsym bro
Outstanding explanation of these 4 proofs. I was trawling CZcams this morning with no success, until I found this video, which explained how to do the proofs at a level I could understand.
i enjoyed the "no u" in the thumbnail, it kept me pushing through XD
This is the best explanation thankyou so much, u got a new subscriber
Thank you, good insight
This was a great video! As an extra note if you are like me then the Proof By Contradiction part around 10 minutes can be tricky when the verbiage is laid out as "Assume that n^2 is even, and n is odd". This is the case because of logical equivalences and De Morgans Law: (p -> q) to -(p -> q) to -(-p OR q) to (--p AND -q) to finally (p AND -q) which is how you end up with the negation of the statement. Hope this helps somebody.
no clue what this means lmao
Second Example is an actual question in my book which I didn’t know how to do , lol thx
To prove Goldbachs conjecture wouldn't we have to be able to find primes by a formula based of prior primes and not the current brute force method of sifting that we do at the moment?
Nice video sir good job sir. Hope you're well.
How did ur a levels go?
have you made a video on proofs including jottings where you work towards an awnser (this isnt part of final working) then work backwards to prove the question (if that makes sense i dont really understand it) no matter how much practice i do i cant seem to get the hang of it
-not sure if this is another way of doing one of these methods or a completely different way (edexel alevel maths)
Interesting question. If you compare a mathematical proof to an essay, you usually write drafts before the final product. Working out a proof can take a lot of work but the proof itself should be neat and tidy like a final draft of an essay
hi, what are all the things that we need to know before answering a proof question, like maths statements
Hi, I believe it is important to know the definitions. Like for a simple example using the first question of proving the even number, first you need to know: what is an even number?
You may answer the sequence of even numbers
2, 4, 6, 8, 10, ...
But what do they all have in common, to be in general form? All of them are multiples of 2, and they would be in the form of 2n where n is the counting numbers 1, 2, 3, ...
So from the above sequence we have
2(1), 2(2), 2(3), 2(4), 2(5),...
4:56 URGENT HELP PLS: i have end of years in like a couple days and i dont get this type of proof: how do you know what cases to use? Like when do i use odd/even cases to cover all natural numbers, when do i use multiples of 3 etc like how did you know that if you prove it for multiples of 3, 1 more than multiples of 3 and 1 less than multiples of 3, that you would answer the question? Since question says multiples of 9 i got confused.
For A level maths there are is a small number of facts that you need to know for these proofs, and I covered most of them in this video. There is a limited set of types of proof questions. It might be easier to chat in discord if you have more questions: discord.gg/HNQrNqfe
@@maths.explained hey ive just read your comments and saw this discord link. just wondering if you have a discord server as the link is invalid?
Yes! Does this work? discord.gg/DCChX9sn I set the links to expire after 7 days just to avoid spam.
@@maths.explained yes it does work, thank you. I have just joined 😌
Which as level maths is easy Cambridge or edexcel?
I think they are probably similar but I have not taught the international AS course no I’m not sure
goldbach's conjecture: could one just prove that the prime digits in the series of positive integers 0-9 are sufficient to create any even positive integer 0-9, then generalize the fact that all integers 9+ are composites of integers 0-9? And then could that not be extrapolated out to positive infinity from there?
Just so you know in maths “composite” has a specific definition. A composite number is any number that is not a prime. Meaning it had more than 2 factors. Most numbers are not composites of integers 0-9. For example 11x13=143.
I understand you mean every number is made up of the digits 0-9. The reason this isn’t very helpful is it doesn’t tell you it’s factors or it’s addends. Look at the number 143. The digits 1,4 and 3 by themselves do not help you find the factors 11 and 13. And they don’t tell you how many ways you can sum other numbers to get 143. Hope that helps.
Could you go over the mock set 2 from last year? Need help with a few aspects
I would love to but I’m a bit sick of getting complaints about posting exams on CZcams if the papers are still “locked” on the Pearson website. If you want you can just say which questions you had trouble with and I can post videos on those topics.
What is a natural number, and where did you get the "all natural numbers are multiples of 3 or 1 less than or more than a multiple of 3"
The natural numbers are the counting numbers 1,2,3,4,5,6 and so on. This video should answer your question: czcams.com/video/4Gw9OzgC7Oc/video.htmlsi=R6ICXGP8aFAUUwhT
sir at 8:58 with n^2 being even meaning that n as even
why cant we assume that n^2 is odd and so n is even as its negation
since 25 is an odd number right?
why does it have to be that n is odd and so n^2 is even
Because we are trying to prove something about n, given a condition about n^2. We are given that n^2 is even.
It’s like when it’s snowing. You might say “it’s snowing, that means it’s cold”. It’s a fact that it’s snowing, and you can prove it must be cold. The negation might be “it’s snowing, that means it’s not cold”. (Well then how could it be snowing?) But you can’t change the fact that it’s snowing. Hope that makes sense.
@@maths.explained IT DOES THANK YOUUUU! YOUR A LIFE SAVER 😭
he explained it good however i couldnt help but stare at my reflection the whole time
lol
I disagree with the proof by contradiction, i don't think "n is odd" is a suitable negation, and would personally negate with "n is not even", allowing for irrational numbers and so forth which were never stated not to be applicable- a proof by counter-example:
if n² is even, then n must be even
Assume n²=2
n²=2(1) => n² is even
Then n=±(2)^½, 2^½ ≠ even
=> if n² is even, n is not necessarily even
Perhaps "if n² is _a perfect square_ and even, n is even" is more suitable
You’re counter example is valid. n does need to be defined as an integer.
I hate proves so much