Question

Write the elements of odd natural numbers less than 10

Answer 1

Answer:

How can I write the set of all odd natural numbers in a set builder as {x|x € N & x is O+}?

First, what is an odd number?

Well, before, let's see what an even number is.

A number n is even if it's a multiple of 2. Meaning that n = 2k where k is an integer.

So, if that's not the case, if n is not a multiple of 2, we say that it is odd.

So, n is odd if n = 2k+1 where k is an integer. Why the plus 1? Because n is not even, there is a remainder, which is 1.

So, here's a way that we can define the set of odd natural numbers.

We want {2n+1 | n€N}.

Let's break this down. We have the set of 2n+1, odd numbers, and we want n to be a natural number, which is why we define n€N.

In fact, we can generalize even and odd numbers to numbers that are multiples of any number, and numbers that have a remainder. For more, research “modular arithmetic”.

Step-by-step explanation:

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