Thank you! This video was very informative! I have my own reason for explaining the reason why your method works for the last 50%. For example in the last question, it states that this statement is *true* for *all values* of m. F states that there's *at least 1 value* that is *false,* but G states that *for all values,* it will be *false.* For the statement to not be *true* for *all values,* it is guaranteed that at least at least *1 value* is *false,* but it is not guaranteed that *all values* are *false.* For the negated circumstance, F will always be true, but G will only sometimes be true (because not all true != all false, but, not all true == at least 1 false). As statement G is only sometimes valid for the negated circumstance, we know that it is not the correct statement. But since F is always valid in the negated circumstance, it must be the negation. At least that's the way I see it. Hopefully that made some sense haha! The video was super helpful in walking through this logic, but it's still super duper weird with their phrasing and all the words, so hard to visualise because they add so many steps o-o
Hi! Just a quick question, for the last question you changed both ‘some k does not’ and ‘for all m’ but in the question before this you only changed ‘some prime’ but not ‘something’, so I wonder if you are still following the rule ‘change as little as possible’😊
I think the rule wasn't really to change as little as possible each time, it was more to claim as little as possible by the end. So in the penultimate one some doesn't change to for all at the end, because that would make a much stronger claim. Whereas in the last one changing for all to some makes the claim weaker, so I did it. Honestly I'm not sure whether even that is completely consistent, I don't know the topic too well, but certainly the principle is not solely to change as little as possible
Love these videos. Genuinely laughed out loud at the “I do proper maths, not this BS” 😂
Thank you, immensely underrated
Thank you! This video was very informative!
I have my own reason for explaining the reason why your method works for the last 50%. For example in the last question, it states that this statement is *true* for *all values* of m. F states that there's *at least 1 value* that is *false,* but G states that *for all values,* it will be *false.* For the statement to not be *true* for *all values,* it is guaranteed that at least at least *1 value* is *false,* but it is not guaranteed that *all values* are *false.* For the negated circumstance, F will always be true, but G will only sometimes be true (because not all true != all false, but, not all true == at least 1 false). As statement G is only sometimes valid for the negated circumstance, we know that it is not the correct statement. But since F is always valid in the negated circumstance, it must be the negation.
At least that's the way I see it. Hopefully that made some sense haha! The video was super helpful in walking through this logic, but it's still super duper weird with their phrasing and all the words, so hard to visualise because they add so many steps o-o
Hi man, love your videos - the work you do is great! Do you think its worth spending time learning about the converse/contrapositive for paper2?
No, not unless you really don't have anything else to spend your time learning
Hi! Just a quick question, for the last question you changed both ‘some k does not’ and ‘for all m’ but in the question before this you only changed ‘some prime’ but not ‘something’, so I wonder if you are still following the rule ‘change as little as possible’😊
I think the rule wasn't really to change as little as possible each time, it was more to claim as little as possible by the end. So in the penultimate one some doesn't change to for all at the end, because that would make a much stronger claim. Whereas in the last one changing for all to some makes the claim weaker, so I did it. Honestly I'm not sure whether even that is completely consistent, I don't know the topic too well, but certainly the principle is not solely to change as little as possible
What 'proper' maths do you do instead of A-level/TMUA maths?
Also, is saying ‘some’ the same as saying ‘there is at least one’, as i’ve noticed that is a phrase that is sometimes used in tmua questions? :)
Yes