# Determine whether the below given statement is true or false. If the statement is false, make the necessary changes to produce a true statement: All irrational numbers satisfy |x - 4| > 0.

Question
Irrational numbers
Determine whether the below given statement is true or false. If the statement is false, make the necessary changes to produce a true statement:
All irrational numbers satisfy |x - 4| > 0.

2021-02-14
If it equals 0 then:
|x-4|=0
Or, x-4=0
Or, x=4
Note that 4 is a rational number. So, for other values of x (except 4) |x-4| will be greater than 0. So, All irrational numbers satisfy |x - 4| > 0. This statement is true.

### Relevant Questions

True or False?
1) Let x and y real numbers. If $$\displaystyle{x}^{{2}}-{5}{x}={y}^{{2}}-{5}{y}$$ and $$\displaystyle{x}\ne{y}$$, then x+y is five.
2) The real number pi can be expressed as a repeating decimal.
3) If an irrational number is divided by a nonzero integer the result is irrational.
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Writing and Proof: If true prove it, if false give a counterexample. Use contradiction when proving.
(a) For each positive real number x, if x is irrational, then $$\displaystyle{x}^{{2}}$$ is irrational.
(b) For every pair of real numbers a nd y, if x+y is irrational, then x if irrational or y is irrational
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a) In the two-sample t test, the number of degrees of freedom for the test statistic increases as sample sizes increase.
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Given each set of numbers, list the
a) natural Numbers
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f) real numbers
$$\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}$$
Which statement is false?
A. every irrational number is also a real number.
B. every integer is also a real number.
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Consider the following statements. Select all that are always true.
The sum of a rational number and a rational number is rational.
The sum of a rational number and an irrational number is irrational.
The sum of an irrational number and an irrational number is irrational.
The product of a rational number and a rational number is rational.
The product of a rational number and an irrational number is irrational.
The product of an irrational number and an irrational number is irrational.
Discover prove: Combining Rational and Irrationalnumbers is $$\displaystyle{1.2}+\sqrt{{2}}$$ rational or irrational? Is $$\displaystyle\frac{{1}}{{2}}\cdot\sqrt{{2}}$$ rational or irrational? Experiment with sums and products of ther rational and irrational numbers. Prove the followinf.
$$\displaystyle{Q}:{\quad\text{if}\quad}{\left\lbrace-\frac{{3}}{{4}},\sqrt{{3}},\frac{{3}}{\sqrt{{3}}},\sqrt{{\frac{{25}}{{5}}}},{20},{1.11222},{2.5015132},\ldots,\frac{{626}}{{262}}\right\rbrace}$$,