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What is true about the sum of 2 odd numbers?
Sum of two odd numbers is always an even number.e.g. 1 + 7 = 8Explanation:The successor of an odd number is an even number and the successor is obtained by adding 1.Let us assume any odd number, say n.On adding 1(i.e. an odd number) to n we get an even number and again on addition of 1 or addition of 2(an even number) to n we get an odd number. If we continue to add like this we get to know that addition of two odd numbers is always an even number.
Why is that there are no consecutive prime numbers?
2 and 3 are consecutive prime numbers; therefore, such a concept does exist, but those are the only two consecutive primes. The reason there are not any others: natural numbers alternate between odd and even numbers. When the number is even, then 2 is a factor. The number 2 is the only even prime number (it's only factors are 2 and 1). All other even numbers have factors, in addition to 2 & 1. So if a number is prime, and the number is not 2, then it is an odd number. The two numbers on either side of an odd number are even. So if the prime number is greater than 3, then the two numbers on either side of it will be even numbers, which are not primes.
How do i solve the set of odd numbers is closed under addition?
You can't. Adding any two odd numbers always gives an even number, which is not a member of the set of odd numbers.
Are even numbers closed in addition?
Yes, they are.
Why is the sum always a even number when you add even numbers?
asking that question is like asking how we know what 2 plus 2 there is no answerYes, there is an answer.To add even numbers is to add sets of two. When you add sets of two, you will always come up with another set of two. Addition of even numbers does not divide the set in two in half, which would result in an odd answer.In Algebra, ax + bx = (b+c)x. If x is two, then we have the addition of even numbers. The result, we see, is divisible by x-two-and thus be an even number.
