I am not sure that I fully unterstand your question but for ordinal numbers it is natural to start like 1, 2, ... or to be more precise first, second, third,... For each object in a set you assign an ordinal number according to some ordering.
For cardinal numbers it is more natural to start like 0,1,2,... because the smallest set is the empty set. Since an empty set has no elements the 'ordinal number' that people often call "zeroth" is of little use because a set of cardinality zero has not "zeroth" element.
Som people in particular in computer science tend start any enumeration by zero, as if they do not distinguish between cardinal numbers and ordinal numbers.
Dear M. Mariappan,
apparently you mention 10 and 9 in decimal numeral system (system, where we use ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to represent any number). To learn more, see https://en.wikipedia.org/wiki/Decimal
Your question sounds like it concerns counting. The digital system was developed for ease of counting and recording. It is convenient to have a few named numbers and make a combination of the few to represent larger counts. The invention of zero as a place holder allows this combination. The place holder convention allows for ease in arithmetic operations. Nevertheless, there are many possible named number combinations that could do away with the place holder. One such system is the simple binary. Binary is usually represent with two named numbers, 1 and 0. Any other pair would do. Up and down arrows could be used. A language for naming numbers must be considered. Suppose you are enquiring about the cost of an object. What would you call a particular set of ups and downs in a verbal conversation?
Zero is not a necessary name for nothing, but would need a representation for some transactions when dealing with ups and downs. A single down could be nothing.
There is no need for negative numbers. An entire mathematical system could be constructed without negative numbers. It is often extremely convenient to perform mathematical operations about a reference point that includes a zero and negative numbers. Indeed, some operations would be unnecessarily difficult without negative numbers. Consider, the manner that the invention of the imaginary number, i, simplified the expression of some physical events.The biggest problem of excluding negative numbers is finding a reference for placing the 1 or a single up arrow.
Why do we use negative and postive infinitives? Its confusing i think only one infinitive in mathematics
M. Mariappan
Infinity and infinitesimals have no physical meaning. They are very large or exceedingly small values. A frame of reference that eases calculation, thereby producing negative numbers does not need to be restricted in the size of the negative or positive values. Mathematically we reach a limiting value that further increase does not change the outcome.
Why should we call it as infinity ?because it is a limiting value or finite value.
Infinity in mathematics is a convenient term and does not mean the same as the vernacular infinity. The meaning of infinity was the subject of several questions on RG. Some want to retain a mythical meaning for mathematical infinity. We should retain the meaning of asymptotic limit. There is no exact finite value to this limit. A large number is relative to the problem. An electron can be excited to infinity (escape the atom) and the distance is very small.
Is electron in system a ground state and excited as surrounding? Is your answer thermodynamically correct?
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