Math, asked by meham1545, 11 months ago

Whole number are closed under dash and dash operation .

Answers

Answered by shivanshusingh97
12

Operations under which a particular set is not closed require new sets of numbers:

Counting Numbers: Subtraction requires 0 and negative integers; division requires rational numbers.

Whole Numbers: Subtraction requires negative integers; division requires rational numbers.

Integers: Division requires rational numbers.

Rational Numbers: All four operations are okay here (with the exception of division by 0). However, solving problems with exponents would require us to expand from the rational numbers. For example, a problem like x2 = 3 can be solved using the real numbers, but not the rational numbers.

Irrational Numbers: All operations require rational numbers.

Real Numbers: All four operations are okay here (with the exception of division by 0).

b.

To go from one set to the next requires new types of numbers:

To go from counting numbers to whole numbers, we need the additive identity 0.

To go from whole numbers to integers, we need the additive inverses -- the opposites of the counting numbers.

To go from integers to rational numbers, we need the multiplicative inverses of all non-zero counting numbers and their multiples. These are fractions with integer numerators and denominators, like 2/3 and -7/4.

To go from rational numbers to real numbers, we need irrational numbers, such as and . Similarly, to go from irrational to real numbers, we need rational numbers.

To go from real numbers to complex numbers, we need i (a number such that when squared it gives -1) and all its real multiples -- the imaginary numbers. Adding any real number and any imaginary number then forms a complex number, for example, 2 + 3i and -2/3 + 2.718i.

Answered by tabarakkhan9082
1

Answer:

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