七年级暑假英语作文（第七周）

作者: 昊哲 | 来源:发表于2022-08-26 14:22 被阅读0次

七年级暑假英语作文（第七周）
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暑假第七周
暑假第七周
暑假第七周
暑假第七周

Last week, Jennet use English to wrote a mass essay, today, I want to challenge writing a math essay.

We all know that root 2 is an irrational number, but, can we prove it? This is what I am going to write about.

First, we need to know what is a rational number. Rational number is a number formed by whole numbers or fractions. So if we wants to prove root 2 is not a rational number, we just have to prove that root 2 is not whole number or fraction.

We know that root 2 is not a whole number, because square of toot 2, which is 2, is greater that 1 square, but smaller than square 2. so root 2 is suppose to be between 1 and 2, and there is no whole number between 1 and 2.So know, we just has to prove root 2 is not a fraction, but this is much more interesting.

In proving this, we have proof by contradiction. It means, if I want to prove that root 2 was not a fraction, we just have to set that root 2 is a fraction, and go on reasoning, and see if we can find a contraction to something we had prove was real or premise. So what is our premise? Is about fraction, about what is a fraction.

If we set root 2 was a fraction, then root 2 can be written as $\frac{b}{a}$ . A and B must be whole numbers, and has to be relatively prime, and, A is not 1. Now, we start roving.

If root 2 is $\frac{b}{a}$ ,

then $2=(\frac{b}{a} )^2$

$2=\frac{b^2}{a^2}$

$2a^2=b^2$

We don't need to know whether $a^2$ is an even number, but we knew that 2 multiplies any non 0 whole number equals an even number. So we can say that $2a^2$ is an even number, and so $b^2$ will be a even number.

And because we knew only even number who multiplies even number can equals an even number. So we can conclude that because $b^2$ is an even number, $b$ will also be an even number.

Continue

$2a^2=b^2$

$a^2=b^2\div 2$

We knew that $b$ is an even number, and even numbers had at least one factor 2 in it. So $b$ can be written as $(2\times m)$ , (m is a non 0 whole number.) So $b^2$ is $(2\times m)^2$ , that is $4m^2$ . So $b^2\div 2=4m^2\div 2=2m^2$

We can get that $a^2=2m^2$ . We don't need to know weather $m^2$ is an even number, we just needs to know $2m^2$ is a even number, because $m^2$ was multiplied by 2.

So we can get that $a^2$ is also an even number, which means $a$ is an even number.

But what is the use of knowing $a$ and $b$ are both even numbers? We set that a fraction has to be relatively prime, but if $a$ and $b$ are even numbers, they can be divided by 2, so the fraction is not relatively primed.

We set up root 2 as a fraction, but we made a contradiction. So root 2 is not a fraction, and since root 2 is also not a whole number, we can get that root 2 is not a rational number.