The density property does not hold for odd numbers in the same way it does for the set of all integers or real numbers. While there are infinitely many odd numbers, they are not densely packed within the integers; there are gaps between them (specifically, every even integer separates two odd integers). Thus, between any two odd numbers, there are even integers, indicating that odd numbers do not form a dense subset of the integers.
The square of an odd number is always odd. This is because when you multiply an odd number by itself, the result retains the property of being odd. For example, squaring the odd number 3 gives 9, and squaring 5 gives 25, both of which are odd numbers. Thus, the pattern holds true for all odd integers.
True
True
False.
When you add three odd numbers, the sum remains odd because the sum of any two odd numbers is always even. Adding a third odd number to this even sum results in an odd number again. This pattern holds true regardless of the specific odd numbers being added, confirming that the sum of three odd numbers is always odd.
True.
No, it is not true: it depends on what your numbers are.
The square of an odd number is always odd. This is because when you multiply an odd number by itself, the result retains the property of being odd. For example, squaring the odd number 3 gives 9, and squaring 5 gives 25, both of which are odd numbers. Thus, the pattern holds true for all odd integers.
It is true that the sum of 2 even numbers is never odd
True
The sum of three whole odd numbers will always be odd keeping in mind that zero is neither even nor odd and that 'null' is not a number.
True
True
Yes.
The GCF is, yes.
False.
Neither. The property of odd or even applies only to integers (whole numbers).