Let A = { -6, - 12/4 , - 5/8 , - √3, 0, 1/4 , 1, 2π, 3, √12}. List all the elements of A that belong to each set. Natural numbers
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Identify the definition of natural numbers: Natural numbers are positive integers starting from 1, 2, 3, and so on.
Examine each element of set A to determine if it is a natural number.
Check if -6 is a natural number: It is not, because it is negative.
Check if -12/4 is a natural number: Simplify to -3, which is not a natural number because it is negative.
Check if 3 is a natural number: It is, because it is a positive integer.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Natural Numbers
Natural numbers are the set of positive integers starting from 1 and going upwards (1, 2, 3, ...). They do not include zero or any negative numbers, fractions, or irrational numbers. Understanding this definition is crucial for identifying which elements from the set A belong to the natural numbers.
Set notation is a mathematical way to describe a collection of distinct objects, known as elements. In this context, the set A is defined with specific elements, and understanding how to interpret and manipulate sets is essential for determining which elements fit the criteria of being natural numbers.
Element membership refers to the relationship between an element and a set, indicating whether the element is part of the set. To solve the question, one must evaluate each element in set A to see if it meets the criteria of being a natural number, which involves checking if it is a positive integer.