Answer
No, we are aging every moment.
Work Step by Step
Some doubt may occur because we use discrete numbers to measure the age of a person: 32 years old, 33 years old, 82 years old, etc. But, no one says: "I am 37.82554 years old".
But, the age of a person is the measure of the time since his or her birth to the present moment, and time is a continuous variable. So, we could say: "I am 45 years, 39 days, 14 hours, 41 minutes, 12 seconds, ...". It only depends on the accuracy of your clock.
