data structures using > you may verify this by substituting the values as shown below < / < / / and / ( < / / < / / < / < / thusin generalwe can write / other useful notations there are other notations like little notation and little notation which have been discussed below little notation this notation provides non-asymptotically tight upper bound for (nto express function using this notationwe write (no( ( )where ( ( ){ (npositive constants cn such that for any and < ( <cg( ) > this is unlike the big notation where we say for some (not anyfor example ( is asymptotically tight upper bound but ( is non-asymptotically tight bound for (nexamples of functions in ( includen log examples of functions not in ( include example show that ( solution by definitionwe have < <cn this is in contradiction with selecting any / an imprecise analogy between the asymptotic comparison of functions (nand (nand the relation between their values can be given asf(no( ( ) ( < (nf(no( ( ) (ng(nf(nth( ( ) (ng(nlittle omega notation (wthis notation provides non-asymptotically tight lower bound for (nit can be simply written asf(no( ( ))where ( ( ){ (npositive constants cn such that for any and this is unlike the notation where we say for some (not anyfor example ( is asymptotically tight upper bound but ( is non-asymptotically tight bound for (nexample of functions in ( ( )includen ( ) ( ) logn ( example of function not in ( ( )is ( (just as example show that / ( solution by definitionwe have <cn / dividing by we get