Hanu walked into the room a little vexed. Ganu, who was reading a book, noticed Hanu’s frustrated expression. “What is going on?” asked Ganu.
“It’s difficult for me to explain to others that the new decade starts on January 1, 2020 and not 2021. How do I explain this to them?” asked Hanu.
“I can assure you it is not easy, as it deals with inequalities and counting, ” said Ganu. “Let me see if I can do this with a simple example–how many numbers are there between 3 and 6?”
Hanu answered, “That’s easy: only two. They are 4 and 5. Now if you had asked me, ‘How many numbers are there between 3 and 6, including the first number?’ I would have answered that there were three numbers: 3, 4, and 5.”
“Yes,” said Ganu, “that is correct. And if we included the last number we would have four: 3, 4, 5, and 6. This is a counting problem; as you can see, if I were to ask you how many numbers are between 0 and 4 (including both), then there are five numbers and not four. But sometimes people think there are only four, because 4-0=4. This came up in the media in a big way, during the change in the millennium. Many people thought that January 1, 2001 was the year the new millennium began, since 2001-1=2000. “
Hanu interrupted, “But they are not including the first year in the subtraction. It should be included!”
“Yes. Similarly, you can understand how people can get confused about the start of the decade. They are simply not including one year. I think you can also extend this to age.”
“Hmmm…wait,” said Hanu. “If somebody is born in 1981, and we wanted to know how old they are in 1987, wouldn’t that depend on the month in which they were born?”
“Yes,” said Ganu, “but even if they were not born on January 1, we can determine how old they will be turning that year. So in 1987, the hypothetical person you mentioned will be turning 7, not 6.”
“Got it,” said Hanu.
“It can be expressed in inequalities as follows,” continued Ganu. “1981 < your current age </= 1987. So that yields six years. But 1981 </= your current age age <= 1987 gives the age 7 years, because it includes the first year. Good luck in convincing your audience about the decades.”