What is the Infimum and Supremum (if there are any) of the following set: {x^4 : x is an element of the real numbers}

Answer 1

The supremum of the set is infinity since if you choose for x the numbers 1,2,3,4,.... we see that there is no upper bound. On the other hand the infimum is equal to zero since for all real numbers x the quantity x^4 is always non-negative and for the choices x=1,1/2,1/3,1/4,... we see that they converge to 0.