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Is there a rational number or an irrational number in mathematics? According to the concept of rational number, any fraction is rational number. But it is irrational number, it should be irrational number.
An irrational number, because it is an irrational number that is infinite uncirculated in its decimal form
Let a be a rational number and x be an irrational number. It is proved that a+x is an irrational number a is zero and ax is an irrational number.
A is not 0?
Prove:(1) Suppose b=a+x is rational number, then
X=b-a.
And because a is a rational number,
So x=b-a is a rational number, and x is an irrational number.
Therefore, the assumption is not true, i.e.
A+x is an irrational number.
(2) When a is not 0, if c=ax is a rational number, then
X=c/a
And because a is a rational number,
So x=c/a is a rational number, and x is an irrational number.
Therefore, the assumption is not true, i.e.
Ax is an irrational number.
= = = = = = =
Inverse method is used to prove irrational numbers.
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