Introduction of odd natural numbers:
In mathematics, there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3,...} according to the traditional definition; or the set of non-negative integers{0, 1, 2, ...} according to a definition first appearing in the nineteenth century.
Odd Natural Numbers:
An odd number is an one kind of integer value that is not consistently divisible by 2. A proper description of an odd number is that it is an integer of the appearance n = 2k + 1, where k is an integer. An even number has the appearance n = 2k where k is an integer.
Properties of odd Natural numbers:
1. Associative law for odd natural numbers:
(x + y) + z = x + (y + z). – Associative law of addition.
(x * y) * z = x * (y * z). - Associative law of multiplication.
2. Commutative law for odd natural numbers:
x + y = y + x. – Commutative law of addition.
x * y = y * x. - Commutative law of multiplication.
3. Cancellation law for odd natural numbers:
If x + y = y + a, then x = y. - cancellation law of addition.
If x * z = y * z, then x = y. - cancellation law of multiplication.
4. Distributive law with multiplication on the left odd natural numbers:
x * (y + z) = x * y + x * z.
5. Distributive law with multiplication on the right odd natural numbers:
(x + y) * z = x * z + y * z.
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Examples for Odd Natural Numbers:
Example 1: closure property in addition:
If 1, 3 are natural numbers, and then 1+ 3=4 is also a natural number
And then,
If 1, 3 are natural numbers, and then 1 * 3 = 3 is also a natural number.
Example 2: commutative property in addition:
If 1, 5 are natural numbers, and then 1 + 5 = 5 +1=6 is also a natural number.
And then,
If 1, 5 are natural numbers, and then 1 * 5 = 5 *1= 5 is also a natural number.
Example 3: associative property in addition
If 1, 3, 5 are natural numbers, then 1 + (3 + 5) = (1+ 3) + 5=9 is also a natural number.
And then,
If 1, 3, 5 are natural numbers, then 1 * (3 * 5) = (1* 3) * 5=15 is also a natural number
In mathematics, there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3,...} according to the traditional definition; or the set of non-negative integers{0, 1, 2, ...} according to a definition first appearing in the nineteenth century.
Odd Natural Numbers:
An odd number is an one kind of integer value that is not consistently divisible by 2. A proper description of an odd number is that it is an integer of the appearance n = 2k + 1, where k is an integer. An even number has the appearance n = 2k where k is an integer.
Properties of odd Natural numbers:
1. Associative law for odd natural numbers:
(x + y) + z = x + (y + z). – Associative law of addition.
(x * y) * z = x * (y * z). - Associative law of multiplication.
2. Commutative law for odd natural numbers:
x + y = y + x. – Commutative law of addition.
x * y = y * x. - Commutative law of multiplication.
3. Cancellation law for odd natural numbers:
If x + y = y + a, then x = y. - cancellation law of addition.
If x * z = y * z, then x = y. - cancellation law of multiplication.
4. Distributive law with multiplication on the left odd natural numbers:
x * (y + z) = x * y + x * z.
5. Distributive law with multiplication on the right odd natural numbers:
(x + y) * z = x * z + y * z.
Between, if you have problem on these topics solving proportions using cross products, please browse expert math related websites for more help on inequality solver with steps.
Examples for Odd Natural Numbers:
Example 1: closure property in addition:
If 1, 3 are natural numbers, and then 1+ 3=4 is also a natural number
And then,
If 1, 3 are natural numbers, and then 1 * 3 = 3 is also a natural number.
Example 2: commutative property in addition:
If 1, 5 are natural numbers, and then 1 + 5 = 5 +1=6 is also a natural number.
And then,
If 1, 5 are natural numbers, and then 1 * 5 = 5 *1= 5 is also a natural number.
Example 3: associative property in addition
If 1, 3, 5 are natural numbers, then 1 + (3 + 5) = (1+ 3) + 5=9 is also a natural number.
And then,
If 1, 3, 5 are natural numbers, then 1 * (3 * 5) = (1* 3) * 5=15 is also a natural number
