Is 0 a natural number?

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Detailed Solution

In many school books, 0 is not a natural number, but in some higher math, 0 is included in the natural numbers by definition. This question depends on the convention your course follows. Primary and middle school materials often define natural numbers as starting from 1, so 0 is excluded. University math or computer science sometimes defines the natural numbers to start at 0 for cleaner formulas and indexing. Because both conventions exist, you should follow your textbook or teacher’s definition to avoid confusion in exams.

Two common conventions

Convention	Definition of natural numbers	Reason
School-level	N = {1, 2, 3, …}	Matches everyday counting that starts at 1
Advanced/CS	N = {0, 1, 2, 3, …}	Simplifies formulas and array indexing

Practical advice

Check your syllabus or the first chapter of your math book.
If the exam uses whole numbers for {0, 1, 2, …}, then natural numbers likely start at 1.
When writing formal answers, state the convention you are using.

So, 0 can be natural in some contexts, but most school exams treat 0 as a whole number, not a natural number.

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