I am a student in computer science and we've already acquired discrete mathematics, computational theory and modern algebra. Consequently, this course is easy for me whereas it is a good opportunity to review these interesting points in this stage. Thank you for your sharing.
cool video! I came to them from the other side (I'm a computer scientist with a math background and was looking up stuff on semigroups). I'm very curious about how you use this in linguistics! You talk about the next video, but I can't find it on the playlist. Is there a next video, or a video where you talk about the applications to linguistics? I'd be very interested to see it!
Quick question for even integers not being a monoid Z, * = 2 * 1 = 1 * 2 = 2 so 1 is a identity element Z, + = 2 + 0 = 0 + 2 = 2 so 0 is a identity element But as per above video, 2Z doesnt have a identity element and hence its a semigroup. Can you please elaborate?
They're identity elements for different operations. Since we're looking at (2Z,*), we must look for the identity element for the * operation (that being the integer 1). Since this is not present in the set 2Z, 2Z does not contain an identity element for the * operation, hence (2Z,*) cannot be a group. If we were looking at (2Z,+), then we would be looking for the identity element for the + operation, which is present in 2Z. Since the other 3 group axioms are satisfied, we have that 2Z is therefore a group. Hope this helps!
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Great vids! U should also continue with ring, field, etc. That'll be very nice ☺️
I am a student in computer science and we've already acquired discrete mathematics, computational theory and modern algebra. Consequently, this course is easy for me whereas it is a good opportunity to review these interesting points in this stage. Thank you for your sharing.
cool video! I came to them from the other side (I'm a computer scientist with a math background and was looking up stuff on semigroups). I'm very curious about how you use this in linguistics! You talk about the next video, but I can't find it on the playlist. Is there a next video, or a video where you talk about the applications to linguistics? I'd be very interested to see it!
At 5:41, you use the inverse.... could you please explain briefly about how inverses work when working with groups ?
Thank you
Great , thanks .
Quick question for even integers not being a monoid
Z, * = 2 * 1 = 1 * 2 = 2 so 1 is a identity element
Z, + = 2 + 0 = 0 + 2 = 2 so 0 is a identity element
But as per above video, 2Z doesnt have a identity element and hence its a semigroup. Can you please elaborate?
1 can't be an identity element of 2Z because 1 is not even, and thus not in the set.
They're identity elements for different operations. Since we're looking at (2Z,*), we must look for the identity element for the * operation (that being the integer 1). Since this is not present in the set 2Z, 2Z does not contain an identity element for the * operation, hence (2Z,*) cannot be a group.
If we were looking at (2Z,+), then we would be looking for the identity element for the + operation, which is present in 2Z. Since the other 3 group axioms are satisfied, we have that 2Z is therefore a group.
Hope this helps!
Could you teach me some problems
what is a dot b ?
you do that when you are proving closedness