Thank you for your excellent content. Question re determining set equality (around 8:44): how do we, in practice, *check all possible x* with the biconditional? Surely there are too many x for an exhaustive check.
Thanks a lot! In practice, we might have more knowledge about the sets we consider and that is what we surely would use then. Of course, I will deal with practical examples later :)
@@angelmendez-rivera351 I had the same question. Shouldn't we always define the set in which x exists before trying to answer a predicate about it? Otherwise, it seems to me that every predicate using "for all" would carry no information.
@@MrOvipare That is a very good question. This gets into some technical and difficult details about quantifiers and domain of discourse. For example, there is no such a thing as a set of all sets. There is a class of all sets, but there is no class of all classes. Quantifying over every mathematical object seems impossible without a well-defined notion of "universe" that can avoid the quantification problem altogether. But you are right: in most contexts, where the domain of discourse is restricted, you can talk about universal quantification by specifying sets, and doing otherwise is completely meaningless.
@@angelmendez-rivera351 interesting, thanks for your input! I’m glad to be visit these topics that were not really covered in my engineering physics program. I’m not entirely sure of what a class is, formally, but that will come soon I suppose!
Could you possible update the quizzes on your Steady to be longer and contain more complex/challenging questions? I am happy to support your channel; however, I find that I learn better when quiz questions require me to take the concepts I've learned and apply them in a new way in order to arrive at the correct answer. Thanks for the any consideration!
If the definition of a subset is only that all values of set A are in set B, cant set B be a subset of itself? Or are subsets not meant to be smaller than the parent set and this is completely valid. I expexted a subset to also be defined as a set which doesnt contain all elements of the parent set.
Thank you very much. I didn't want to confuse people, so I only have Steady (which works exactly like Patreon). For all other people, I just have Paypal: www.paypal.com/paypalme/brightmaths Thanks for asking and please enjoy the videos :)
Can't stop hearing "pretty cat"😁
I feel the same ;)
Cat Love
Same here.
I really enjoy the way you’ve presented set theory using logic. Have not seen it done this way before! Thank you
Great lecture, as always.
Very good introduction to sets
Thank you for your excellent content. Question re determining set equality (around 8:44): how do we, in practice, *check all possible x* with the biconditional? Surely there are too many x for an exhaustive check.
Thanks a lot! In practice, we might have more knowledge about the sets we consider and that is what we surely would use then. Of course, I will deal with practical examples later :)
For All x in set A (we can see the set above) are planets, Why is it False should it be True? 6:18
It did not say "for all x in set A," it merely said "for all x."
@@angelmendez-rivera351 I had the same question. Shouldn't we always define the set in which x exists before trying to answer a predicate about it? Otherwise, it seems to me that every predicate using "for all" would carry no information.
@@MrOvipare That is a very good question. This gets into some technical and difficult details about quantifiers and domain of discourse. For example, there is no such a thing as a set of all sets. There is a class of all sets, but there is no class of all classes. Quantifying over every mathematical object seems impossible without a well-defined notion of "universe" that can avoid the quantification problem altogether. But you are right: in most contexts, where the domain of discourse is restricted, you can talk about universal quantification by specifying sets, and doing otherwise is completely meaningless.
@@angelmendez-rivera351 interesting, thanks for your input! I’m glad to be visit these topics that were not really covered in my engineering physics program. I’m not entirely sure of what a class is, formally, but that will come soon I suppose!
for me: x = {2, 4, 6, 8,..} so both are false
amazing. Gracias
Thanks a lot :)
شكرا و جزاك الله خيرا
RIP Pluto
Thanks
Could you possible update the quizzes on your Steady to be longer and contain more complex/challenging questions? I am happy to support your channel; however, I find that I learn better when quiz questions require me to take the concepts I've learned and apply them in a new way in order to arrive at the correct answer. Thanks for the any consideration!
Thank you very much! I am working on more exercises regarding the videos :)
Danke schön
Is the null set a subset of every set? Why?
Is it safe to say the statement "all objects"?
Is the statement assert that there is a set consist of all objects?
It is always good to think in sets. However, for understanding quantifiers, you can just start think of x being anything.
Isn't it impossible for a set to include infinity as an element?
Hello. I have never seen such a set: {2, 2, 2, 3, 3, 5}. What did you mean here?
Do values in quantifiers have domain ?
like ∀x : x - 1 < x, can x here be anything or can we specify to it to some domain
In this writing x can be anything. However, usually later it always comes from a set.
If the definition of a subset is only that all values of set A are in set B, cant set B be a subset of itself? Or are subsets not meant to be smaller than the parent set and this is completely valid. I expexted a subset to also be defined as a set which doesnt contain all elements of the parent set.
Yes, equality is definitely possible. It like the less or equal sign ≤
@@brightsideofmaths Thank you for the fast response, you explained it in the next video immediately haha.
Great content. Do you have a patreon account that people can support you on?
Thank you very much. I didn't want to confuse people, so I only have Steady (which works exactly like Patreon). For all other people, I just have Paypal: www.paypal.com/paypalme/brightmaths
Thanks for asking and please enjoy the videos :)
Isn't the notion of "infinity" logically a predicate with no definite meaning?
No
2:32 I like that😍💋 💝💖❤️