Reciprocal means to set a number mathematically, and its product X is 1, which is recorded as 1/X. The process is "multiplication inversion". All numbers except 0 have reciprocal, and the numerator and denominator are in opposite phases. The two products are1,and 0 has no reciprocal.
The reciprocal is a number, and its product is 1, that is, if the product of the reciprocal of a number x and x is 1, then the number x is called reciprocal. For any nonzero real number x, we can find a number 1/x, so that x times 1/x equals 1. If x is zero, then x multiplied by 0 equals 0, but no number can multiply 0 by this number to get 1. Therefore, zero has no reciprocal.
The definition of reciprocal is the product of 1. Multiplying zero by any number (including yourself) to get 0 does not meet the definition of reciprocal. We can conclude that zero has no reciprocal.
The origin of reciprocal can be traced back to medieval Europe, which was first proposed by the French mathematician Joseph Cassirer. /kloc-in the 0/7th century, when French mathematician Joseph Cassirer was studying prescriptions, he thought of a new concept, namely reciprocal. He named this concept inverse power, which means that finding the inverse power of a number is finding the reciprocal of this number.
Cassirer's concept had a profound influence on mathematics. Subsequently, British mathematicians John Napier and Henry Briggs widely applied the concept of reciprocal in the study of logarithm, which further promoted the development of reciprocal in the field of mathematics.
The function of reciprocal:
1 and reciprocal can solve the problem of infinite division. In the division of integer and divisible decimal, the division can be easily converted into multiplication by reciprocal, thus avoiding the problem of infinite division. For example, we can convert 10/3 into 10×( 1/3), and then we can calculate the result.
2. The reciprocal can be used to calculate the value of the score. The reciprocal of a fraction can be obtained by inverting the numerator and denominator. For example, if the numerator of a fraction is A and the denominator is B, then its reciprocal is B/A. Therefore, if you need a fractional value, you only need to multiply its reciprocal by the denominator to get the result.
3. Reciprocal can be used to prove some mathematical formulas and properties. Multiplicative commutative law and associative law can be proved by reciprocal. In addition, reciprocal can also be used to prove some inequalities and equations. For example, the monotonicity of hook function and some properties of inequality can be proved by reciprocal.