Consider the following multiple choice question:
c.) all of the above
d.) none of the above
I’ll give you time to answer.
The resistance against zero can be noted even at the architectural level in buildings where the ground-level is rarely denoted as the zeroth-level as it should be. However, for mathematicians it comes easily to label the floors of a building to include zero, for example, the Department of Mathematics' building at the University of Zagreb in Croatia has floors numbered as -1, 0, 1, 2, and 3. In fact, this is not a particularity of one building but a common practice in modern buildings in large cities such as Buenos Aires. In most European countries the floors are always numbered starting from 0. We do have a special word to say 'ground floor' in a conversation, not using 0, but the elevators will always offer you a "0 button" for the ground floor.
The origin of the fallacy that any number divided by zero is equal to infinity goes back to the work of BhÃ¡skara, an Hindu mathematician who wrote in the 12th century that
"3/0 = ¥, this fraction, of which the denominator is cipher is termed an infinite quantity". He made this false claim in connection with an attempt to correct the wrong assertion made earlier by Brahmagupta of India that A / 0 = 0.
Notice that by this fallacy one tries to define "infinity" in terms of zero. Unfortunately, similar practices seem to prevail to the present day. A similar fallacy exists for logarithms of zero which is believed by many to be (negative) infinity.
The notion of zero was introduced to Europe in the Middle Ages by Leonardo Fibonacci who translated from Arabic the work of the Persian (from Usbekestan province) scholar Abu Ja'far Muhammad ibn (al)-Khwarizmi (the word "algorithm," Medieval Latin 'algorismus', is a contamination of his name and the Greek word arithmos, meaning "number,: has come to represent any iterative, step-by-step procedure) who in turn documented (in Arabic, in the 7th century) the original work of the Hindu mathematician Ma-hÃ¡vÃral as a superior mathematical construction compared with the then prevalent Roman numerals which do not contain the concept of zero. When these scholarly treatises were being translated by European accountants, they translated 1, 2, 3, ....; upon reaching zero, they pronounced, "empty", Nothing! The scribe asked what to write and was instructed to draw an empty hole, thus introducing the present notation for zero. Hindu and early Muslim mathematicians were using a heavy dot to mark zero's place in calculations. Perhaps we would not be tempted to divide by zero if we also express the zero as a dot rather that the 0 character.
The development of this number is now known to have occurred in many cultures independently around the world – not just in Western mathematics. This includes the Mayan people of Central America.
They developed a counting system that used dots, lines, and a drawing of a shell. Each dot represented one, a line represented five, and the shell represented zero. These symbols were grouped together to form a base 20 number system. The system appears more complicated than the decimal system, and also has a strong link to astronomy.
Hindu mathematicians in southern India first created zero, but did not recognize it as a number. They used zero only as a placeholder when no number existed. Add 4 + 6. You get 10, 1 in the tens column and none in the ones column. The Hindus realized that they needed a way to indicate that there was no number in units position. They called it "sifr", their word for an empty place... Before AD 800 the Hindu number system migrated west into the Arab world. There a brilliant mathematician, al-Khwarizmi, invented zero as a number. He realized that it had to be a number in order for the emerging system of algebraic equations to work. Algebra, another word first used by al-Khwarizmi, comes from Arabic, al-jabra, and means the reduction, or the solution.
Now the ancient Greeks began their contributions to mathematics around the time that zero as an empty place indicator was coming into use in Babylonian mathematics. The Greeks however did not adopt a positional number system. It is worth thinking just how significant this fact is. How could the brilliant mathematical advances of the Greeks not see them adopt a number system with all the advantages that the Babylonian place-value system possessed? The real answer to this question is more subtle than the simple answer that we are about to give, but basically the Greek mathematical achievements were based on geometry. Although Euclid's Elements contains a book on number theory, it is based on geometry. In other words Greek mathematicians did not need to name their numbers since they worked with numbers as lengths of lines. Numbers which required to be named for records were used by merchants, not mathematicians, and hence no clever notation was needed.
Ptolemy in the "Algamest" written around 130 AD uses the Babylonian sexagesimal system together with the empty place holder 0. By this time Ptolemy is using the symbol both between digits and at the end of a number and one might be tempted to believe that at least zero as an empty place holder had firmly arrived. This, however, is far from what happened. Only a few exceptional astronomers used the notation and it would fall out of use several more times before finally establishing itself. The idea of the zero place (certainly not thought of as a number by Ptolemy who still considered it as a sort of punctuation mark) makes its next appearance in Indian mathematics.
The story of zero is an ancient one. Its roots stretch back to the dawn of mathematics, in the time thousands of years before the first civilization, long before humans could read and write. But as natural as zero seems to us today, for ancient peoples zero was a foreign--and frightening--idea. An Eastern concept, born in the Fertile Crescent a few centuries before the birth of Christ, zero not only evoked images of a primal void, it also had dangerous mathematical properties.
In the beginnings of human history there was a long stretch of time in which zero was not needed, therefore it was not introduced as a concept at all. However when it was introduced, it frightened people both mathematically and philosophically, for it symbolized nothingness, and for many cultures, nothingness symbolized death and chaos.
When the Yorktown's computer system tried to divide by zero, 80,000 horsepower instantly became worthless. It took nearly three hours to attach emergency controls to the engines, and the Yorktown then limped into a port. Engineers spent two days getting rid of the zero, repairing the engines, and putting the Yorktown back into fighting trim.
No other number can do such damage. Computer failures like the one that struck the Yorktown are just a faint shadow of the power zero. Cultures girded themselves against zero, philosophies crumbled under its influence, for zero is different from the other numbers. It provides a glimpse of the ineffable and the infinite. This is why it has been feared and hated--and outlawed.