Question 1. For some integer m, every even integer is of the form

Solution:

To show that every even integer can be expressed in the form of $$2m$$ for some integer $$m$$, we can follow these steps:

1. Understanding Even Integers:
An even integer is defined as any integer that is divisible by 2. This means that when you divide an even integer by 2, there is no remainder.

2. General Form of Even Integers:
We can express any even integer mathematically. If we take an integer $$m$$, then multiplying $$m$$ by 2 gives us an even integer. Thus, we can write:
$$\text{Even Integer}=2m$$
where $$m$$ is any integer.

3. Examples of Even Integers:
Let’s consider some examples:
– If $$m=0$$, then $$2m=2\times 0=0$$ (which is even).
– If $$m=1$$, then $$2m=2\times 1=2$$ (which is even).
– If $$m=2$$, then $$2m=2\times 2=4$$ (which is even).
– If $$m=-1$$, then $$2m=2\times -1=-2$$ (which is even).
– If $$m=-2$$, then $$2m=2\times -2=-4$$ (which is even).

4. Conclusion:
Since we can find an integer $$m$$ for every even integer, we conclude that every even integer can indeed be expressed in the form $$2m$$.

Final Statement:
Therefore, every even integer is of the form $$2m$$ for some integer $$m$$.