mystic few examples F orphan effort is - and squared + 3 + + afford somewhat there's a function so 2 N squared + 3 + + 4 is less than 2 and squared plus 3 and squared + 4 n square so thus to N squared + 3 + + 4 is less than equal to 9 and square for all and greater than equal to some value can find out from this value starting and just put one there so this is greater than equal to this one so this is C and this is G of n so it is a fourth and this big o of G of n so G of n is what and squared F of n is Big O of N squared now pops a function I can say - N squared + 3 + + 4 is greater than equal to 1 into n square so it is omega and squared so again I can write Omega N squared I made it as 1 into n squared now sinking - N squared plus 3 n plus 4 is like in between 1 and n square + 9 and square so this is Theta of n square n square on both the sides next if a fortune is n Square log n + n then n Square log + + n is less than equal to 10 M Square log n I just and here it is less than equal to one N squared log in so put aside a god and square log in and then square login and this is a smaller this is greater than this one and this is smaller than this one so put aside a got N squared log in an N squared log n so this is Big O of n Square log in and Omega N squared log in as well as this is teat off and squared log n so all three have written them together here now if you observe in our this orders we have not written n Square log n but if I write n square Logan comes in between n square and NQ n Square log n is greater than n square but less than and Q so this is the combination of N squared and Logan and for this also you can specify the class here in between those two you can mention a class this if a function is n factorial then let us see and factor is nothing but n into n minus 1 into n minus 2 a who goes on to 3 and so if I write in reverse then 1 into 2 into 3 goes on go and now this is really less than equal to what see as a practice what we were doing everything we were making it as n so here also I will make it as and into N and this is less than equal to what so other practice will make everything as 1 into 1 into to hold on to one so they say they get 1 and this is n factorial and Isis and ba n now for this one for n factorial I don't have any smaller value here and I have to take it as bun and if I take larger value this n power n upper bound is n power n and put the side I'm not getting same thing I am NOT getting same thing if I get same thing then I can take it as theta so what I can write I can write B go off and power N and Omega 1 so the lower bound for n factorial is a 1 upper bound for n factorial is n power n right so here we cannot find a tight bond or average bond or theta for n factorial so if you try to put n factorial here plus is not there for n factorial but if you try to put it there then for the smaller values of n it will be nearer to this one and for the larger values of and it will be increasing and going up to and power n so you cannot fix a particular place for n factorial you cannot say that n factorial is always greater than and power 10 and less than n power 11 you cannot say that you cannot find a place for it you cannot find a place for it right so it's greater than or equal to 1 but less than equal to n power n so upper bound is n fallen and a lower bound is 1 so this is the function for which you cannot find the theta so now upper bound and lower bound are useful as they already told that when you cannot mention theta bomb for any fun then we go for upper bound and lower bound so yes here we have taken upper bound and lower wonderful function the state log n factorial so for log n factorial if I write log of 1 into 2 into 3 and so on to n then this is less than or equal to log off as the practice will make everything as n so n into n into so on to end and it is less than log 1 into 1 e 2 so on to 1 so this side will be 0 but we write 1 and this is log of n factorial and this is less than equal to this is log of n raised to n and that will be written as n log n therefore comes on this side and is n log n so now you can see that for n log n factorial also upper bound is log n power N and the lower bound is 1 and there is no time bomb for this function so the factory function we cannot define the Titebond so we go for upper bound as an organ and lower bound as one so there is no time for so now you have understood when you use Big O notation when you use Omega and all these theta is preferable if you are able to find theta for any function that's better because that is a time bomb and if you are using upper bound we will also try to use a time bomb do not give a very far a larger ready and fingered one don't give any smaller value try to give a nearest value for a function suppose your function is n square so try to give it n square only Dover writing and Morgan or n no root n is also correct true but not meaningful but not useful if I ask you that I want to buy a mobile phone for my requirement what could be the better price so any price for my phone that's available in the market so suppose you have some idea what the mobile phone and you said that you can buy out well for around twenty thousand so you are giving me nearest figures if I say if you don't know the B this figures and if I ask you tell me something minimum so you are saying that eighteen nineteen thousand or magazine all you can say twenty one twenty four thousand like that so you are nearer only but if we say many moments then two thousand three thousand so your answer is correct I can get some mobile phone into three thousand not so smart phone also but that will not be a suitable one for me but your answer is right but it's not useful and if I ask maximum so you say well that do that so even for one left will have mobile phones are available answer is correct but not meaningful for me so same way when you have any function and square then you can say n square that is the answer perfect answer so given theta is the right one but if you're writing Omega so I am not sure whether you are giving me nearest or not that's the problem will be go it may be nearest one and maybe bigger than that one also but kita guarantees that you have given the exact figure exact notation exact time complexity when you are using Omega then also it means that you may be giving a lower value may or may not be nearest one so that's why big Omega use when you're not sure about the exact one right that is the meaning it case so that is much much suitable for n factorial n log n factorial but you can use them for any purpose it's not a rule that you must not use you must use three tolerably you can use any notation so when you're using Omega means may be a minimum this one and maybe it is more than this the time may be more than this also that's the meaning tetons exactly this Mustang so hope you have understood this topic this is very very important topic now I'm coming leader at its next video you can find the properties of asymptotic notations you can watch that video