13:44 Let b be any arbitrary number , then for ba=b(ae)=b(ea)=(be)a by left cancellative law, b=be this also needs to be added to prove for any arbitrary element of G
sir in case of identity the way u derived identity is based on hypothetical like u assumed there might be any identity that will exist but what if in set there is no element on which if we do operation it will give the same element?
If your doubt is related to 12:35, then yes there will always be such element by closure. If it's general doubt, then, if there exists Nonsuch element, then identity won't exist
Sir, don't we have to prove that identity is unique? As, during prove of identity, we assume there should be some element such that ae = a but would that e be same for all other element, don't we need to prove that?
That may be proved as well. As this semi group if finite and satisfies cancellation law, thus ae1=a=ae2 means e1=e2 .As such we just have to find an identity while proving a set to be group, Anupam
@@rampravesh3823 go through whole syllabus and practice examples, you will better know utility of calculator. This is more useful in numerical analysis, matrix etc.
13:44 Let b be any arbitrary number , then for ba=b(ae)=b(ea)=(be)a by left cancellative law, b=be this also needs to be added to prove for any arbitrary element of G
Sir, is it enough to show ae=ea to prove that identity is unique?
As if there are multiple identities then ae would not be equal to ea right?
@@soumilsaxena4062 we need to show that e is unique thats why random b is taken
by right cancellation
Carry on sir it will very helpful for us ..IAS lagne ke bad appse milne jarror auunga ...
All the best :)
sir plz continue it....thanku so much sir
It will be resumed in October, Shivani.
sir in case of identity the way u derived identity is based on hypothetical like u assumed there might be any identity that will exist but what if in set there is no element on which if we do operation it will give the same element?
If your doubt is related to 12:35, then yes there will always be such element by closure.
If it's general doubt, then, if there exists Nonsuch element, then identity won't exist
Thanku sir 🙏🙏
Sir, don't we have to prove that identity is unique? As, during prove of identity, we assume there should be some element such that ae = a but would that e be same for all other element, don't we need to prove that?
That may be proved as well. As this semi group if finite and satisfies cancellation law, thus ae1=a=ae2 means e1=e2 .As such we just have to find an identity while proving a set to be group, Anupam
@@Mathocrat Thank you sir.
@@Mathocrat Sir, here it seems 'e' is unique for 'a' but could you explain how it is the same for other elements?
@@13Charlievalid doubt. Please refer pinned message.
@@Mathocrat Thanks sir!
7:41 sir agar hm poore real numbers ke liye dekhenge to semi group cancellation law hold karte hue group ho skta hai ??
Thank you sir
Sir I have a question...
Do calculators are allowed in Maths optional paper...?
yes, it's allowed.
@@learn_GS just confirming... thanks
Calculator kis topic me use kroge brother 🤔🤔🤔🤔🤔🤔🤔
@@rampravesh3823 go through whole syllabus and practice examples, you will better know utility of calculator. This is more useful in numerical analysis, matrix etc.
Thank you sir.