It is if we only consider integers. If we consider all real numbers, for example, it would not be.
Any set of three odd integers must be odd - for example, 3 + 5 + 7 = 15. Similarly, the sum of an even number of odd integers added together will always be an even integer.
ODD Integers are those numbers that end in 1,3,5,7,9. So a set of ODD integers could be (101, 99, 93, 103, 10,005, 57) et seq/.
No because 2 is an even integer
There is no set of three consecutive even integers whose sum is 999. There are two other sets; one is odd, the other is mixed. The odd set is 331, 333 and 335. The mixed set is 332, 333 and 334.
There is no set of three consecutive odd or even integers whose sum is negative 31.
The set of positive odd integers.
There is no set of two consecutive odd integers for 323. The set has one odd and one even integer. The numbers are 161 and 162.
There is no set of four consecutive odd integers for 204. The only set is even: 48, 50, 52 and 54.
For positive integers, if the least significant bit is set then the number is odd, otherwise it is even. For negative integers in twos-complement notation, if the least significant bit is set then the number is odd, otherwise it is even. Twos-complement is the normal notation, allowing a range of -128 to +127 in an 8-bit byte. For negative integers in ones-complement notation, if the least significant bit is set then the number is even, otherwise it is odd. Ones-complement is less common, allowing a range of -127 to +127 in an 8-bit byte, where 11111111 is the otherwise non-existent value -0 (zero is neither positive nor negative). Ones-complement allows you to change the sign of a value simply by inverting all the bits. Twos-complement is the same as ones-complement but we also add one. Thus the twos complement of 0 is 0 because 11111111 + 1 is 0 (the overflowing bit is ignored). 11111111 then becomes -1 rather than the non-existent -0.
There is no law of closure. Closure is a property that some sets have with respect to a binary operation. For example, consider the set of even integers and the operation of addition. If you take any two members of the set (that is any two even integers), then their sum is also an even integer. This implies that the set of even integers is closed with respect to addition. But the set of odd integers is not closed with respect to addition since the sum of two odd integers is not odd. Neither set is closed with respect to division.
Any set of three odd integers must be odd - for example, 3 + 5 + 7 = 15. Similarly, the sum of an even number of odd integers added together will always be an even integer.
There is a set of two consecutive integers that have a sum of 123; one odd and one even. They are 61 and 62.
No. For example, 5 is an odd integer and 3 is an odd integer, yet 5/3 is neither an integer nor odd (as odd numbers are, by definition, integers).
ODD Integers are those numbers that end in 1,3,5,7,9. So a set of ODD integers could be (101, 99, 93, 103, 10,005, 57) et seq/.
No because 2 is an even integer
No. It can be infinite, finite or null. The set of odd integers is infinite, the set of even integers is infinite. Their intersection is void, or the null set.
There is no set of three consecutive even integers whose sum is 999. There are two other sets; one is odd, the other is mixed. The odd set is 331, 333 and 335. The mixed set is 332, 333 and 334.