Let {{MATH_7}} be a function with domain {{MATH_8}} and range {{MATH_9}}: {{CMD_10}} {{ENV_11}} {{CMD_12}} Let {{MATH_13}} be a function with domain {{MATH_14}} and range {{MATH_15}}: {{CMD_16}} {{ENV_17}} {{CMD_18}} We say that {{MATH_19}} and {{MATH_20}} are {{CMD_21}} of each other if {{MATH_22}} for all {{MATH_23}} in {{MATH_24}}, and also {{MATH_25}} for all {{MATH_26}} in {{MATH_27}}. Sometimes we write {{MATH_28}} in this case. {{CMD_29}} {{ENV_30}} {{CMD_31}} and {{CMD_32}} {{ENV_33}} {{CMD_34}} So, we could rephrase these conditions as {{MATH_35}} {{CMD_36}} These two simple equations are somewhat more subtle than they initially appear.