A few days ago

Jerse

Is it true that no two persons are exactly the same height?

I just read that “fact” in my college textbook and it blew my mind.

It was saying you can be 67 inches, 67.75 in., 67.7555757in., 67.755575755575775757757575775757575in. but never the same exact height as someone else – living or dead.

Can someone clarify?

Top 10 Answers

A few days ago

Expat Mike

Favorite Answer

Consider two facts:

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.

A few days ago

will T

If you get down to millionths or even billionths of an inch, there are so many possible heights that it is unlikely for 2 people to be EXACTLY the same height – it’s not true to say that it has defiantly never happened, but it is a strong mathematical probability that (as long as you break the unit of measurement down far enough) no 2 people have ever been the same height.

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.

A few days ago

Stephen H

Given the worlds population, both current living and total historical, it is incomprehensible that there aren’t MANY individuals of exactly the same height at any given moment, no matter HOW ridiculously far past the decimal you carry it What is the name of the textbook you refer-to? Just because it appears in a textbook, even a college textbook, doesn’t necessarily make it the truth. I’ve pen-and-ink corrected more than a few college textbooks in my time, and a few professors as well.

A few days ago

BeatTheGib

No it’s not true. In many cases, a child will grow to be taller than their parents. Think about it. As that child grows and starts to approach the height of his or her parent and eventually surpasses the height of the parent, at some point, they are the exact same height. The child doesn’t skip over the height that their parents happen to be.

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″.

A few days ago

TurtleFromQuebec

If you are growing up and eventually get taller than your mom, then necessarily at some point you must be the same height as her (this is called the Intermediate Value Theorem in beginning calculus). So the statement in your textbook is a bit tricky. They are trying to tell you that height is a real number and experimentally real numbers can’t be measured exactly, but you shouldn’t think too hard about what they are saying!

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

A few days ago

Tom

I have 3 answers, all could be argued to be correct.

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.

A few days ago

Anonymous

Well, we don’t usually measure to the nearest trillionth of an inch, so what you say could be true if you look really closely. But for the usual tape measure, there has to be someone in all the billions of people on earth that is the same height as you, though perhaps not to the nearest billionth of an inch.

A few days ago

banjuja58

I agree with Tom’s third possibility. Mathematically speaking, at some point in time, the growing person is precisely the same height as the person whose height remains stable.

A few days ago

sirbobby98121

YOU are not the same height…

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

Shorter at night after a day of being vertical.

4 years ago

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Is it true that no two persons are exactly the same height?

Is it true that no two persons are exactly the same height?

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