You wrote AXB = BXA while explaining at the same time, that they are not equal. I was looking for the correction, but it never came. I hope people didn't find this confusing, at least noone has complaint about it. Great videos!
Good catch, I totally forgot to put the slash through it. Or, given how I underlined it a moment later, I wrote the equality because I was planning to say this is true sometimes, but not generally, which is probably the wrong way to explain it, since the emphasis should be placed on it not being true generally.
Thank you for another clear explanation about the Cartesian Product of Sets. I have been a huge fan of the mathematical videos made by you for quite a long time. All of them are really helpful!
I decided to split your request into two videos, so as to not rush either topic. This first one is on relations, but I do touch on what makes a relation a function, and hope that will help. I will be away from home for the next few days, and will probably not be able to record the lesson on functions until I return. Until then, hopefully this lesson on relations is helpful! Please don’t hesitate to ask any questions in the comments. What is a Relation? | Functions and Relations ua-cam.com/video/6uxbY_nPwgU/v-deo.html
Great video. The best explanation among the 5 videos I watched, specially the bit at the end, where you explained the X and the Y axis. Nobody did that.
Thanks a lot Ankita, so glad it was clear! Anytime someone gives an especially strong or specific compliment to a lesson, I usually check the lesson out to see for myself what I did - and I have to say I was cringing at my handwriting in this one haha! My videos look much nicer now!
@@WrathofMath I will check out your other videos. Writing isn't important as long as it is legible. It's the context you provide to the math. For instance, I saw many videos which explained Cartesian product, but what exactly is Cartesian about it, why call it that was the source of confusion. The last bit was helpful in that sense. I will check other videos as I need them.
Thanks for the vid....I had a question. My math teacher told me that in sets,neither order nor repetition is of any relevance and that sets are equal if they have the same elements order and repetition not withstanding..... Doesn't that mean that Cartesian products are commutative?
Thanks for watching and good question! Cartesian products are not commutative. It's correct that order does not matter in the set, but a set could be composed of elements, like ordered pairs, where order does matter. Suppose A = { 1 } and B = { 2 }. Then AxB = { (1, 2) } and BxA = { (2, 1) }. It is true that { 1, 2 } equals { 2, 1 }. However, (1, 2) does not equal (2, 1), so those are distinct elements. Hence { (1, 2) } and { (2, 1) } are distinct sets. Does that help?
You wrote AXB = BXA while explaining at the same time, that they are not equal. I was looking for the correction, but it never came. I hope people didn't find this confusing, at least noone has complaint about it. Great videos!
Good catch, I totally forgot to put the slash through it. Or, given how I underlined it a moment later, I wrote the equality because I was planning to say this is true sometimes, but not generally, which is probably the wrong way to explain it, since the emphasis should be placed on it not being true generally.
Thank you for another clear explanation about the Cartesian Product of Sets. I have been a huge fan of the mathematical videos made by you for quite a long time. All of them are really helpful!
Oh my God, sir I wanted this video..Thankyou so much.🙏🏻🙏🏻
You're welcome! I'm glad to deliver the goods!
@@WrathofMath Sir please make a video on Relations and Functions.
Good request, I've been wanting to make such a video, I'll get to it ASAP!
@@WrathofMath Thank you sir.
I decided to split your request into two videos, so as to not rush either topic. This first one is on relations, but I do touch on what makes a relation a function, and hope that will help. I will be away from home for the next few days, and will probably not be able to record the lesson on functions until I return. Until then, hopefully this lesson on relations is helpful! Please don’t hesitate to ask any questions in the comments.
What is a Relation? | Functions and Relations ua-cam.com/video/6uxbY_nPwgU/v-deo.html
Great video. The best explanation among the 5 videos I watched, specially the bit at the end, where you explained the X and the Y axis. Nobody did that.
Thanks a lot Ankita, so glad it was clear! Anytime someone gives an especially strong or specific compliment to a lesson, I usually check the lesson out to see for myself what I did - and I have to say I was cringing at my handwriting in this one haha! My videos look much nicer now!
@@WrathofMath I will check out your other videos. Writing isn't important as long as it is legible. It's the context you provide to the math. For instance, I saw many videos which explained Cartesian product, but what exactly is Cartesian about it, why call it that was the source of confusion. The last bit was helpful in that sense.
I will check other videos as I need them.
You are saving my grades!
Glad to help!
BEST EXPLAINATION
Simple to understand, thank you
Great video!! Very well explained.
Thank you!
Thanks so much! Most helpful video on Cartesian products 🥳
Glad to hear it was helpful! Thank you for watching!
@@WrathofMath my pleasure!!!
awesome video helped a lot. thanq
Glad it helped, thanks for watching!
Thank you, Professor.
Glad to help!
Beautiful and explicit
Thank you for watching!
you are amazing tutor, thx
Thanks for watching!
My savior.
Just doing my job, thanks for watching! Let me know if you have any questions!
this has been very helpful thankyou and i like the song that you play at the end of your videos how can i download it
Thank you 😊
This is cool! I've been looking for this one. Thank you for sharing this to us, it really helps.
So glad it helped, thanks for watching!
Is there an example from physics that shows Cartesian multiplication?
Thanks for the vid....I had a question. My math teacher told me that in sets,neither order nor repetition is of any relevance and that sets are equal if they have the same elements order and repetition not withstanding..... Doesn't that mean that Cartesian products are commutative?
Thanks for watching and good question! Cartesian products are not commutative. It's correct that order does not matter in the set, but a set could be composed of elements, like ordered pairs, where order does matter.
Suppose A = { 1 } and B = { 2 }. Then AxB = { (1, 2) } and BxA = { (2, 1) }.
It is true that { 1, 2 } equals { 2, 1 }. However, (1, 2) does not equal (2, 1), so those are distinct elements. Hence { (1, 2) } and { (2, 1) } are distinct sets. Does that help?
@@WrathofMath So I take them as points in a Cartesian plane?
Thanks!
Glad to help, thanks for watching!
What app u use???????
i love you
love you too, thanks for watching!