Mathematics

The Importance of zero in Mathematics



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The idea of zero has existed as long as mathematics. People have always know when they ran out of food. It has not always been a defined concept. That idea has only been around for the past 2600 years or so. The primary way that most people encounter zero is as a filler between another number and a decimal point.

Zero is pretty handy here. It holds the place of empty values. For example 100 in the decimal notation tells us that there are no values in the 1's or 10's but there is a 1 in the hundreds. So, we read it as one hundred. No one ever says one hundred no tens and no ones. Conversely, on the other side of the decimal point, .001 becomes one thousandth. There are no tenths and no hundredths. Useful little thing isn't it!

In graphing, zero marks the place where an axis is intersected. If the vertical axis is crossed, then X becomes zero. If the horizontal axis is crossed, then Y becomes zero. Most lower algebra equations are solved by finding the zeros. In 3 dimensional graphing the concept continues with the third axis. Zero is the concept behind factoring polynomials and using the quadratic formula. It even shows up when using the Fundamental Theorem of Calculus.

Some higher level equations can only easily be solved by putting in a well-placed zero by inserting a +1 and -1 at different points along the polynomial. An easy illustration of this idea is the 3 brothers who inherited , 1/3, and 1/6 of a herd of 17 horses. They were perplexed until the day that a neighbor road up on his horse. He said, "I can solve this." He put his horse in the stable with theirs. This made 18 horses. He gave 9 to the first brother, 6 to the second brother, and 2 to the third brother. That made 17 horses, and he road his home. It's not a perfect example, but you get the idea.

Zero is often not so important by itself, but in relationship to other numbers. A couple of examples have already been used. When dealing with limits, velocity, and acceleration, the direction that movement has in relation to zero, dictates whether it is positive or negative. Often the importance of how small a number is becoming is not so important as the direction it is going when approaching zero.

In accounting, zero is important because it is the place at which your budget is exceeded or exhausted. It also is the point that divides profit from loss. Many times in new ventures, the point where the losses become a zero is objective that must be reached to determine if the venture is worthwhile. This often involves a 3 or 5 or 10 year horizon depending on the type and size of the business.

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