Significance
Even though zero has the power to destroy the logic behind mathematics (as you have explored in the Explanation of Mathematics tab), it also has made things possible that we could not have discovered without it. The invention or discovery of zero made it possible for algebra and other calculations to be done on paper without the need for a physical object to calculate. It also has led to the introduction and useful meaning of negative numbers. Since zero is the fulcrum between the negative and positive numbers, we know for example that when we balance our checkbooks, if we get zero as an answer, then we do not owe anyone money but nor do we have any more money to spend. Zero brings meaning to the phrase “breaking even”.
Without zero we would not be able to write numbers in their decimal forms. Thus, our calculations for making different materials would not be very precise and the growth of industry would likely not have advanced as rapidly as it did (Chuck, 2012). Among many other advantages that understanding of zero as a number gives us is technology and the computer itself. The first computers that were invented were based on the idea of determining whether something was there or not. The first computer language was a binary system of zeros and ones where zeros represented an empty slot and a one meant that it was full. To list all the advancements that zero has made possible would be impossible, and yet we are still discovering more about this puzzling number every day.
Application:
Since there are so many applications and ways in which zero has advanced mathematics, here we explore only one application that I discovered while working on this project. This application comes from the use of zero in differentiable calculus. Because of zero, we can create equations representing profit and cost and determine how to get the most profit out of a business. For example, check out this Khan academy video on maximizing profit for a shoe company:
Although zero is one of the most frustrating numbers to work with at times, such as trying to divide by it, it has brought about mathematics that would not have been possible without it. It is truly one of the greatest discoveries and influential numbers in the history of mathematics, and it still contains great value and worth to us today.