Presentation On Numbers Basic Summary: On Numbers By Priyank Shah

What is a Number ? A number is a mathematical item that is used for counting and measuring. In mathematics, the definition of number has been drawn-out over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.

Natural numbers The numbers that are familiar to us are the natural numbers or counting numbers: one, two, three, and so on. Usually, the sequence of natural numbers started with 1 (0 was not even considered a number for the Ancient Greeks.) In the 19th century, set theorists and other mathematicians started including 0 in the set of natural numbers The base ten numeral system, is almost universal use today for mathematical operations, the symbols for natural numbers are written using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In this base ten system, rightmost digit of a natural number has a place value of one, and every other digit has a place value ten times that of the place value of the digit to its right.

Integers Integers are formed by the natural numbers (including 0) (0, 1, 2, 3,...) are the positive numbers together with the negatives of the non-zero natural numbers (−1, −2, −3,...).They are Viewed as a subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {..., −2, −1, 0, 1, 2,...}. The set of all integers is often denoted by a boldface Z.

Rational numbers Rational number is a number which can be expressed as a fraction with an integer numerator and a non-zero natural number denominator. Fractions are also written as two numbers, the numerator and the denominator, written as m ⁄ n. m represents same parts, where n equal parts of that size make up one whole. Two different fractions may correspond to the same rational number; for example 1 ⁄ 2 and 2 ⁄ 4 are equal

Real numbers The real numbers include all of the measuring numbers. Real numbers are usually written using decimal numerals, in which a decimal point is placed to the right of the digit with place value one. Each digit to the right of the decimal point has a place value one- tenth of the place value of the digit to its left. Thus represents 1 hundred, 2 tens, 3 ones, 4 tenths, 5 hundredths, and 6 thousandths. In saying the number, the decimal is read "point", thus: "one two three point four five six ". In the US and UK and a number of other countries, the decimal point is represented by a period, whereas in continental Europe and certain other countries the decimal point is represented by a comma. Zero is often written as 0.0 when it must be treated as a real number rather than an integer. In the US and UK a number between −1 and 1 is always written with a leading zero to emphasize the decimal. Negative real numbers are written with a preceding minus sign: Every rational number is also a real number.

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