There are six billion people in this world. Assuming that all of their heights were evenly distributed between 4’8″ and 6’8″, you would find 250 million people within every span of one inch. (actually, heights bunch up at averages and you’d likely find alot more between 5’8″ exactly and 5’9″ exactly, but for our purposes we’ll say 250 million, because I don’t have the real numbers anywhere).

So now you have to measure within at least a 250-millionth of an inch in order for that theory to possibly be true. If you measured with less accuracy, you’d by definition have to get duplicates.

OK, so you have people running around whose heights differ by one billionth of an inch. Now you have to consider the fact that over the course of a day, people’s heights can vary by as much as 1/4 of an inch. Over the span of a day and all that variation, the odds of no two of these people ever having the same height for even a second would be around 0.0000000000000000000001%, give or take.

So it’s conceivably possible, but the odds are better that the sun will suddenly turn blue tomorrow for no reason.

Having said that – how do you measure your height? – due to compression of the spine you are shorter at night than you are when you first get up in the morning.

So if a baby is born at 21 inches long and grows up and is 6’2″ fully grown, that person will have been every height from 21 inches to 6’2″.

If you are actually taking beginning calculus you can impress (or annoy) your instructor with what I said.

Yes, it is true that if you could measure the height of every person living and dead to a very very high degree of accuracy none would be the same.

No, in reality the most accuracy we could measure someones height to would be about 1/100th of an inch. At this accuracy there would definitely be more than one person with the same height.

No. In one scenario I thought of you could have one person overtaking a second person in height. Therefore, at some minute point in time both people were exactly the same height.

you are taller in the morning – your spine is relaxed.

Shorter at night after a day of being vertical.