A Quiz about Nothing

Answer: even

One common test to determine if a number is odd or even is to divide it by two. If nothing is left over, it's an even number. Zero meets the definition of an even number using this test. A second test is that an odd number is defined as an even number plus one. Adding one to zero results in a sum of 1, which is an odd number because it can't be evenly divided by 2.

It is also true that numbers generally alternate in sequence--odd, even, odd, even. Zero would fall into an even place in sequence with the numbers on either side of it.

There are people who feel that zero cannot be put into either category, but my research indicated that the prevailing consensus among mathematicians is that zero is even.

Answer: Neither

Intuitively, it makes sense that zero is neither positive nor negative. One could say zero exists at the border of positivity and negativity but partakes of neither quality (although I don't know why anyone would WANT to say that!)

Answer: It was discovered by several different cultures.

While there isn't perfect agreement on this point, it's generally acknowledged that zero was discovered as a mathematical entity independently three times: by the Babylonians in Mesopotamia around 300 B.C.; by the Mayans in Central America around 350 A.D.; and again in India around 458 A.D.

There is some disagreement about the latter instance's being an independent discovery, as some scholars opine that there was dissemination of the knowledge of zero from the Babylonians to India.

Answer: All of these.

Of course, people had a concept of "nothing" (as in, "Do you have any vegetables to sell me?" "No, I have none."), but it wasn't incorporated into mathematics (as in 3 x 0 = 0) or used as a place holder until its "discovery".

Answer: It didn't.

Actually, for the man on the street, nothing much happened. There was no sweeping international clarification or transformation of mathematic thought. Indeed, the idea of zero pops up in a number of cultures and then disappears again for decades or even centuries.

Answer: An early treatise setting forth the rules concerning zero.

The Rules of Brahmagupta, published in 628 A.D., also known as Brahmasphutasiddhanta (The Opening of the Universe), covered many topics related to astronomy and mathematics. It set forth such concepts as X + 0 = X, X - 0 = X, and X x 0 = 0. It also proposed that X / 0 = 0, which is not generally accepted in mathematics today.

Answer: Dividing by zero leads to many contradictions in our system of mathematics.

This is a big topic outside the purview of these comments to explain fully, but: one argument is that to divide something means to distribute it into a number of shares, like cutting a pie into sixths to make six shares. Dividing by zero is NOT distributing anything (or to put it REALLY confusingly, there is an absence of distribution), so no division is taking place. Another way to look at this is that division yields a ratio of two numbers, say, R=A/B. Basic math tells us that if R=A/B, A=R*B. If B=0, A must also equal 0 for the second statement to be true. If A and B equal zero, in the first equation we can't determine what R is, and in the second, R can be any number at all. For our general everyday mathematics to hold up internally, we need a unique solution--or at least a finite number of solutions-- to that second equation.

Answer: It enabled greater ease of expression and calculations with numbers.

Again, it's beyond the scope of this comment to explain this fully, but think of this: the Roman numeral for 327 is CCCXXVII. Which is easier and more efficient to write down? That's ease of expression. Now try multiplying 327 by 102. In Roman terms, that would be CCCXXVII x CII. How are you going to proceed, exactly? That's ease of calculation. Zero's introduction into mathematical use allowed the concept of a place holder for the first time. Roman, and other numeric systems that lacked zero, did not.

In the number 102 (we all know this nowadays from elementary school!), the zero in the middle represents that there are no 10s in the number. There is one 100 and there are 2 ones. But in the Roman representation of 102, we have only C representing one hundred and II, representing two.

There is no representation of the unused 10s place in their system.

Answer: Undefined

Mathematics at times employs "conventions", which are mathematical assertions that have not been proven true, but without them, our mathematics wouldn't work. (It's helpful here to remember that the root of the word "convention' is the same as that of the word "convenience").

In the case of zero to the zero power, sometimes it works better to have it equal 1 and sometimes it's better to have it be indeterminate. I must confess that the mathematics behind this is out of my league, but what I did learn is that sometimes mathematicians work within a system that requires zero to the zero power to equal 1 and sometimes they don't. (I swear I am not making this up!) Another way to put this, I guess, would be, whatever floats your boat.

Answer: All are probably correct.

But, Gloriosky, Zero! Wasn't it an illuminating quiz nonetheless? If you liked it, send me a note about nothing!