Give an example of a well-defined set (using description) that cannot be written using the roster method. Explain why it cannot.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Many sets can be expressed using roster notation.

For example, the set {elements in water} has {hydrogen, oxygen} as its roster notation. The set {positive multiples of 3 that are less than 20} is {3, 6 ,9, 12, 15, 18} in roster form. Even many infinite sets can be expressed in roster form with the help of ellipsis. For example, the  set {whole numbers larger than 9} has {10, 11, 12, 13, ... } as its roster notation. 

But not every set can be expressed in roster notation.

Give an example of a well-defined set (using description) that cannot be written using the roster method. Explain why it cannot.

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