Let be an integer variable which tends to infinity and let be a continuous variable tending to some limit. Also, let or be a positive function and or any function. Then Hardy and Wright (1979) define
1. to mean that for some constant and all values of and ,
2. to mean that ,
3. to mean that ,
4. to mean the same as ,
5. to mean , and
6. to mean for some positive constants and .
implies and is stronger than .
The term Landau symbols is sometimes used to refer the big-O notation and little-O notation . In general, and are read as "is of order ."
If , then and are said to be of the same order of magnitude (Hardy and Wright 1979, p. 7).
If , or equivalently or , then and are said to be asymptotically equivalent (Hardy and Wright 1979, p. 8).