Discrete Math - 9.5.1 Equivalence Relations

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Күн бұрын

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@luisdrg6995 3 жыл бұрын

In example 1, Another way to find if it's Symmetric: aRb -> bRa (a - b) -> (b - a) Note that (b - a) can also be written as -(a - b). Since we assumed that (a - b) is an integer, we can say that -(a - b) is a negative integer. Therefore, it is symmetric :)

@zzeynep2813 3 жыл бұрын

I have watched from Turkey. Your examintaion is very helpful and clear. Thank you. I hope that I take high points from the midterm about Relations :)

@freddiemercury5501 15 күн бұрын

Hangi üni

@OIW Күн бұрын

Thank you so much. I understood everything which happens rarely. You are pretty good

@SizakheleMakhasi 2 ай бұрын

Thank you very much teach, have a midterm test in few hours, really helped.❤

@polarbear986 2 жыл бұрын

Woww, you are so generous for creating and sharing these videos🙏 Thank you so much. I'm having a discrete math exam soon. I find your teaching very helpful!!

@merlenye6347 4 жыл бұрын

This is extremely helpful! Thank you!

@ifeomaveronicaobialunamman2938 4 жыл бұрын

I totally love your videos! Clearly understood!

@mathsplus01 2 жыл бұрын

Very clear video. I can use this in my tutoring. Thank you

@curious6678 6 ай бұрын

I don't understand how this is even fair if for one example we're choosing same numbers to prove the relation is right and in another example choosing different number to prove it's wrong 💀

@omrifishbein7159 2 жыл бұрын

In 16:45 a class [0] is referred to. Since 0 is not a member of the set this I think is a mistake. Should be for example [3] or [6]...

@PoPo-tc8ir 2 жыл бұрын

agree

@mutebiernest-i9d Ай бұрын

Thank you very much, your videos are helpful and i understand more better

@AhmedSalah-yd8di 3 жыл бұрын

you are the best

@noofalmalki4531 Күн бұрын

In 6:40 just completely assuming we have the l(c)=7 doesn’t make sense.. l(c) could be any number thus we don’t know if it’s transitive or not . the question never implied that c is the same as b .. so we can’t just say l(b)=l(c)

@SawFinMath Күн бұрын

Yes. That is how transitive works. IF a implies b, and b implies c, meaning we assume that a implies b and b implies c.

@malihays Ай бұрын

hello professor!! thank you 4 u videos, they are my savior. I was wondering, will you post partial ordering & hasse diagram?

@SawFinMath Ай бұрын

@@malihays not at this time. I’m trying to keep up with my precalc playlist but am looking at a possible channel membership where I create videos like this for members.

@malihays Ай бұрын

@@SawFinMath this would be great!!

@MathCuriousity 11 ай бұрын

Hey! If you have a moment, may I ask a question: let’s say we have an equivalence relation aRb. Why can’t I represent this within set theory as set T comprising subset of Cartesian product of a and b, mapped to a set U which contains true or false? Thanks so much!!

@StoneColdMagic 3 жыл бұрын

Yet another excellent video. Thank you!. :) I find that it's a common theme when I study these topics . . . why? What's the point? What is the purpose of an equivalence relation, and what's the purpose of a partition? Why do we study them, and what are real world uses/examples of them? Thanks again!

@SawFinMath 3 жыл бұрын

Because we are math dorks?

@reconvene4 3 жыл бұрын

@@SawFinMath This earned a sub. Great video :)

@StoneColdMagic 3 жыл бұрын

@@SawFinMath - Funny. So true. However, this is a question I hear fellow students ask all the time, and I've never heard a good answer from another professor, so I'm curious what is the application for this stuff?

@luisdrg6995 3 жыл бұрын

Relations can be used to solve problems such as determining which pairs of cities are linked by airline flights in a network, finding a viable order for the different phases of a complicated project, or producing a useful way to store information in computer databases. In some computer languages, only the first 31 characters of the name of a variable matter. The relation consisting of ordered pairs of strings where the first string has the same initial 31 characters as the second string is an example of a special type of relation, known as an equivalence relation. Equivalence relations arise throughout mathematics and computer science. Copy & Paste straight from the textbook^^^^

@johnywaves 3 жыл бұрын

Thank you. thank you. thank you. You make this so easy to understand

@ddharsh2548 Жыл бұрын

excellent explanation!!!

@nangalucia7lucia667 3 жыл бұрын

Thanks very much. Ur video was helpful indeed

@rachelvanderlely6324 3 жыл бұрын

You're the best!

@SawFinMath 3 жыл бұрын

Thanks!

@panashemureyi2584 2 жыл бұрын

so when you get to a[4] the values are the same with a[0]. 19:25

@zeynepergul4768 Жыл бұрын

12 : 20 why didnt we think if a and b are equal to each otther and only write the oppossite values

@brormaos8616 4 жыл бұрын

thank you for the videos, teacher :)

@berkouklahcene2594 2 жыл бұрын

Professor i have a question, how to determine the number of equivalence classes in a set ?

@StoneColdMagic 3 жыл бұрын

I loved your answer to my question about why. Because we are math dorks! :) However, I really would like to know if there is a real answer to this. I find it very common that fellow students say "I understand the concept, but what's the point?" And inevitably, the professor does not have an answer. I've asked professors at school. I've asked (comments) other KZbinrs, and nobody seems to have an answer. :( What's the real-world application for all this Discrete Math stuff? Thanks for all the great content!

@makaylabullock2961 3 жыл бұрын

Its actually very much similar to computer/programming logic. If you can understand the logic and functionality behind the programming/coding it's easier to put together your programs as well as take them apart and understand all the pieces that went into it. Currently, that is the direct application I've seen with it and used it for.

@buh357 Жыл бұрын

You can apply discrete math to understand programming language.

@StoneColdMagic Жыл бұрын

@@buh357 - I get that. Hence my question. How do equivalence relations relate to / help us understand programming?

@moski9861 Жыл бұрын

@@StoneColdMagic I hope you are satisfied with this answer from ChatGPT.: Equivalence relations can be useful in programming in various ways. Here are a few examples: Testing equality: In programming, we often need to compare two values to check if they are equal. Equivalence relations provide a formal definition of what it means for two objects to be equivalent, which helps us design and implement tests for equality. For example, in Python, the == operator tests for equality, which is based on the equivalence relation of identity (two objects are equal if they have the same identity) or value (two objects are equal if they have the same value). Grouping objects: In some cases, we want to group objects together based on their properties. Equivalence relations allow us to partition a set of objects into equivalence classes, where each class contains objects that are equivalent to each other. This is useful in data analysis, clustering, and other applications. For example, we might group a set of integers into equivalence classes based on their parity (even or odd). Object-oriented programming: In object-oriented programming, we often define classes that represent abstract concepts or entities. Equivalence relations can help us define the behavior of objects of a class. For example, we might define a class of geometric shapes and specify that two shapes are equivalent if they have the same area. Hashing: In some programming contexts, we need to store and retrieve objects quickly based on their values. Hashing is a technique that maps an object to a unique integer based on its value. Equivalence relations can help us design hashing functions that are consistent (two equivalent objects should have the same hash value) and efficient (the hash function should minimize collisions between different objects).

@RA-hn1wm Жыл бұрын

@@StoneColdMagici think it is like the arrays concept in java not really sure tho

@gbemisolaagboola8255 4 жыл бұрын

at 10:38 in Transitiv example , what rules says the number has to be 16?,what if its say 7

@DevProTips 4 жыл бұрын

It has to be some number that 8 divides (for example, 16, 24, 32, etc.). It is given that _a_ divides _b_ and _b_ divides _c._ Using that information, you need to be able to conclude that _a_ divides _c_ as well. [To show this you can say, _a_ goes into _b_ some number of times, _m,_ and _b_ goes into _c_ some number of times, _n,_ and because of that, the number of times _a_ goes into _c_ is _m*n._ Since two integers _m_ and _n_ multiplied together result in an integer, you can say _a_ divides _c_ and therefore the relation is transitive.