Closure Property

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A Closure is a function object that remembers values in enclosing scopes even if they are not present in memory. Let us get to it step by step Firstly, a Nested Function is a function defined inside another function. It's very important to note that the nested functions can access the variables of the enclosing scope.

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.Properties of rational numbersRational means anything which is completely logical whereas irrational means anything which is unpredictable and illogical in nature. The word rational has evolved from the word ratio. In general, rational numbers are those numbers that can be expressed in the form of p/q, in which both p and q are integers and q≠0. We can denote these numbers by Q.

Closure propertyFor two rational numbers say x and y the results of addition, subtraction and multiplication operations give a rational number. We can say that rational numbers are closed under addition, subtraction and multiplication. For example:. (7/6)+(2/5) = 47/30. (5/6) – (1/3) = 1/2. (2/5).

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Closure Property

(3/7) = 6/35Do you know why division is not under closure property?The division is not under closure property because division by zero is not defined. We can also say that except ‘0’ all numbers are closed under division. Commutative lawFor rational numbers, addition and multiplication are commutative.Commutative law of addition: a+b = b+aCommutative law of multiplication: a×b = b×aFor example:Subtraction is not commutative property i. This can be understood clearly with the following examplewhereasThe division is also not commutative i.e. A/b ≠ b/a as,whereas,Associative lawRational numbers follow the associative property for addition and multiplication.Suppose x, y and z are rational then for addition: x+(y+z)=(x+y)+zFor multiplication: x(yz)=(xy)z.Some important properties that should be remembered are:. 0 is an additive identity and 1 is a multiplicative identity for rational numbers. For a rational number x/y, the additive inverse is -x/y and y/x is the multiplicative inverse.