# Mathematical Reasoning True or False? There exist irrational numbers with repeating decimals? There exists a natural number x such that y > x for every naural number y?

Mathematical Reasoning
True or False?
There exist irrational numbers with repeating decimals?
There exists a natural number x such that for every naural number y?
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

lamanocornudaW
Step 1
Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.
To find the given statement is true or false,
There exist irrational numbers with repeating decimals.
By definition of rational number,
A number that can be express as a ratio p/q where p and q are integers such that is called a rational number.
A number thet can not be expressed as a ratio of two integers is called an irrational number.
Step 2
Let a number with repeating digits, where a is any digit from 1 to 9.
Multiply x by 10 on both sides:

Now consider:

Thus, we can write the repeating decimal number
That means every repeating decimal number is a rational number.
Therefore, the given statement There exist irrational numbers with repeating decimals is False.