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# 数学代写|离散数学代写Discrete Mathematics代考|MATH200 Variables

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## 数学代写|离散数学代写Discrete Mathematics代考|Variables

A variable is sometimes thought of as a mathematical “John Doe” because you can use it as a placeholder when you want to talk about something but either (1) you imagine that it has one or more values but you don’t know what they are, or (2) you want whatever you say about it to be equally true for all elements in a given set, and so you don’t want to be restricted to considering only a particular, concrete value for it. To illustrate the first use, consider asking
Is there a number with the following property: doubling it and adding 3 gives the same result as squaring it?
In this sentence you can introduce a variable to replace the potentially ambiguous word “it”:
Is there a number $x$ with the property that $2 x+3=x^2$ ?
The advantage of using a variable is that it allows you to give a temporary name to what you are seeking so that you can perform concrete computations with it to help discover its possible values. To emphasize the role of the variable as a placeholder, you might write the following:
Is there a number $\square$ with the property that $2 \cdot \square+3=\square^2$ ?
The emptiness of the box can help you imagine filling it in with a variety of different values, some of which might make the two sides equal and others of which might not.

## 数学代写|离散数学代写Discrete Mathematics代考|Writing Sentences Using Variables

Use variables to rewrite the following sentences more formally.
a. Are there numbers with the property that the sum of their squares equals the square of their sum?
b. Given any real number, its square is nonnegative.
Solution
a. Are there numbers $a$ and $b$ with the property that $a^2+b^2=(a+b)^2$ ?
Or: Are there numbers $a$ and $b$ such that $a^2+b^2=(a+b)^2$ ?
Or: Do there exist any numbers $a$ and $b$ such that $a^2+b^2=(a+b)^2$ ?
b. Given any real number $r, r^2$ is nonnegative.
Or: For any real number $r, r^2 \geq 0$.
$O r:$ For every real number $r, r^2 \geq 0$.