@@solmathsolutions hello thanks a lot for your videos and efforts, if i didn't misunderstand i assumed that the question is about is it possible for us to find different identity elements in some questions i'm also asking this for group definition in abstract math is there any circumstance that different identity elements may be found while checking the given set is whether a group or not under the given operation thanks..
@@sadececansu9 It's an easy early proof in group theory that the identity element is unique. If you assume there are two identity elements, e and f, then you say definition of identity is that e * a = a - so what happened if you take a to be the "other" identity element f. Ok, so then e * f = f. If you consider that f is also an identity element, you have that a * f = a for all a in G, so in particular when a = e you have e * f = e. Put these two equation together and you have e = e * f = f, so that e = f. So there can actually only be one identity element in a group. I think in semigroups it is possible to have left-sided identities, right sided identities and also different two-sided identities, because if there are not inverses you can't do the cancellation which is necessary to make this proof work in group theory.
Ur teaching is awesome luv it❤
I appreciate you from the bottom of my heart
I've been struggling with the basic ideas of binary system,but your videos help me a lot
Thanks a lot it's very understandable
Please have you also explained the inverse
Yes.
Please find the link to the inverse video below 👇
ruclips.net/video/zvVUIxKJGC0/видео.html
Good work, keep it up
Thank u very much sir well appreciated
God bless you sir
Wao
Wow good 👌 plz can u help me to solve 5*(-5) where a*b=a+b+3ab.
5*(-5)=5+(-5)+3(5)(-5)
=5 - 5 + 3(-25)
=0 - 75
= -75
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Thank tout you
Thank you so much
Please can there identity element be different
Come clear with your question, please
@@solmathsolutions hello thanks a lot for your videos and efforts, if i didn't misunderstand i assumed that the question is about is it possible for us to find different identity elements in some questions i'm also asking this for group definition in abstract math is there any circumstance that different identity elements may be found while checking the given set is whether a group or not under the given operation thanks..
@@sadececansu9 It's an easy early proof in group theory that the identity element is unique. If you assume there are two identity elements, e and f, then you say definition of identity is that e * a = a - so what happened if you take a to be the "other" identity element f. Ok, so then e * f = f. If you consider that f is also an identity element, you have that a * f = a for all a in G, so in particular when a = e you have e * f = e.
Put these two equation together and you have e = e * f = f, so that e = f. So there can actually only be one identity element in a group.
I think in semigroups it is possible to have left-sided identities, right sided identities and also different two-sided identities, because if there are not inverses you can't do the cancellation which is necessary to make this proof work in group theory.
The question is not clear
Which of the questions please?