I have looked at videos, websites and books trying to understand this and I come across this video, only 7 minutes long and understand it. Thank you so much!
Randell! I just discovered your channel because of this video, since there are only very basic tutorials on this topics, but this is exactly what I needed! It is great you chose three typical exam questions, since this is what really helps to clarify if one has understood it! This was very much appreciated mate! Thank you so much1
This question was asked in quiz yesterday. I thought it was the toughest question in the quiz and I left it blank but now I have realized that it was the easiest one! :D
For the last question what if you chose c to be 5.7 or 5.8, then wouldn't that would make it an equivalence relation? How do you know which numbers to pick
For something to be an equivalence relation the three rules must apply in ALL cases. So to show that something is NOT an equivalence relation we only need to exhibit one case where one or i more of the rules don't apply.
Extremely helpful video! Although for the example disproving an equivalence relation, shouldn't we not use numerical values to show reflexivity and symmetry check out? Playing with numbers helps to give us an idea, but isn't solid enough to check them off.
Hi. To prove that the relation is not an equivalence relation it is only required to show that it is not reflexive OR is not symmetric OR is not transitive. You don't need to show that all 3 properties are untrue. So my numeric example showing a lack of transitivity is sufficient to answer the question properly (and get full marks).
Randell Heyman hello! Yes that I’m aware of, and we only need to show that it fails transitivity or something else. But we also said it didn’t fail reflexivity or symmetry through using specific numbers
@@martinecampbell4502 I only used the numbers in the case of reflexivity and symmetry to explain that it was unlikely that we would be able to prove that either of these fail. For an exam or test it would be sufficient to just write down some numbers to show that transitivity does not exist in all cases.
I'm not asleep, I'm awake. But I'm awake inside of a nightmare-equivalent. Not a nightmare, but a nightmare-equivalent. It's inside of a nightmare-equivalent that the terror that I could feel could be just as great as it would be inside of a nightmare. It's inside of a nightmare-equivalent that a desperation that I could feel to escape from it could be just as great as it would be inside of a nightmare. (As a matter of fact, the desperation that I could feel right now to escape from this particular nightmare-equivalent _is_ the desperation that I _do_ feel right now to escape from it.) If I wake up out of a nightmare to what has in it something common to a nightmare (e.g., terror, desperation, and hopelessness) then I can legitimately reference that what I wake up to is a nightmare-equivalent. That's the way that I see it. If I sound crazy it's probably because I am.
You claimed symmetry in the final example, but you hand picked numbers that were less than 1 apart. If you had picked 3.1 = a, and 5 = b, then it wouldn’t be symmetric, right?
Great video! Just one question. Do you always try to prove true? In the last example, I used a = 5.1 and b = 2.9 and the absolute value of their difference is clearly greater than one. Could I have stopped the proof there?
No. That's not correct. To show a relation is not an equivalence relation you need to show that it is not reflexive OR it is not symmetric OR it is not transitive. For this question the relation is reflexive and symmetric but not transitive. I prove that it is not transitive with a counterexample.
@@RandellHeyman So basically you have to prove reflexibility, symmetry, and transitivity must always be true in order to prove something is has equivalence relation?
@@adeelali8417 Yeah but there are cases that exist which can prove its reflexive OR symmetric but there are none that can prove its transitive. So essentially you have to show that yeah it can be reflexive and yeah it can be symmetric but since its not transitive (i.e. all three are not applicable) therefore not an equivalence relation.
Hi. On the second last line I show that a-c is an integer. If you simplify the first equality you get a-c=a-c which is what you should get but it tells you nothing. I am not sure where you got a-c=a+c. I hope that helps.
Hi. To prove something is an equivalence you have to show it satisfies the 3 rules in every case. So you woukd normally to use s proof. To show something is not an equivalence relation you only have to exhibit one case where one of the 3 rules doesn't apply. Hope that helps.
