QuestionIs it true or false that every irrational number is a natural number? Choose: True or False.
Studdy Solution
STEP 1
Assumptions1. We understand the definition of an irrational number. . We understand the definition of a natural number.
STEP 2
Define an irrational number.
An irrational number is a number that cannot be expressed as a ratio of two integers. In other words, it cannot be written in the form , where and are integers and . Examples of irrational numbers include , , and .
STEP 3
Define a natural number.
A natural number is a number that is used for counting and ordering. In common mathematical terminology, words colloquially used for counting are "cardinal numbers" and words connected to ordering represent "ordinal numbers". The natural numbers include all the positive integers from1 upwards1,2,3,,5,6, etc.
STEP 4
Compare the definitions of irrational numbers and natural numbers.
From the definitions, we can see that an irrational number cannot be a natural number because an irrational number cannot be expressed as a ratio of two integers, while a natural number is a positive integer.
STEP 5
Based on the comparison, we can conclude that the statement "Every irrational number is a natural number" is false.
The correct answer is False
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