Matemáticas
What Is an Integer?
Integers are the whole numbers and their negatives: …, −2, −1, 0, 1, 2, …. Zero is one of them, and so is 3.0, because 3.0 and 3 are the same number.
Integer
An integer is any number in the list …, −3, −2, −1, 0, 1, 2, 3, … — a whole number, positive, negative or zero, with no fractional part.
- Dónde lo encuentra el alumnado
- Grade 5 and 6 mathematics, when negative numbers first appear on the number line, and again at IGCSE, where questions on types of number hand you a list and ask which entries are integers.
La respuesta corta
An integer is a whole number with no fractional part, including negatives and zero: …, −3, −2, −1, 0, 1, 2, 3, …. So 7, 0 and −412 are integers, while 3.5, 2/3 and √2 are not. Zero is an integer, and so is 3.0, because 3.0 and 3 are the same number.
Un ejemplo
Integers: −412, −4, 0, 19, 3.0 Not integers: −4.5, 2/3, √7, 0.1
3.0 sits in the first list because a decimal point is a piece of writing, not a property of the number. Three pounds written as £3.00 on a receipt is still three pounds. √7 sits in the second list because it is 2.6457… and never resolves into a whole number, however far the decimal is taken.
The list, and what falls off it
The integers are a single list, evenly spaced, running away from zero in both directions and stopping nowhere. Between two neighbours there is no third integer: 2 and 3 sit next to each other, and everything in the gap — 2.1, 2.5, 22/7 — is some other kind of number.
The useful thing to hold on to is that integer describes the number, not the way it happens to be written. 6/2 is an integer, because 6/2 is 3. 0.5 + 0.5 is an integer, because it is 1. A student who classifies by appearance will get both of those wrong, and the fix is to work the value out first and classify afterwards.
Is zero an integer? Is 3.0?
Yes to both, and they are the two questions that come up every time the word is taught. Zero sits in the middle of the list. It is neither positive nor negative, which is a separate fact and the source of the confusion, but it is unarguably an integer.
3.0 is an integer for the reason above: it names the same number as 3. The only time the trailing zero carries any extra meaning is in measurement, where 3.0 cm is a claim about how precisely something was measured. That is a statement about accuracy, not about what sort of number you are holding.
The symbol, and where you meet the word in an exam
Mathematicians write the set of all integers as ℤ, from the German Zahlen, meaning numbers. The natural numbers sit inside ℤ, and ℤ in turn sits inside the rational numbers, so calling something an integer is a stronger claim than calling it rational.
In Cambridge IGCSE Mathematics 0580 the word turns up in the types of number strand, where a question gives a short list and asks you to pick out the integers, the primes or the irrationals. The Sets topic on the same syllabus brings the braces and the element symbol with it, so a condition can be written as a line of notation rather than a sentence.
Preguntas frecuentes
Is zero an integer?
Yes. Zero is in the list of integers, sitting between −1 and 1. It is the only integer that is neither positive nor negative, and that is what makes students hesitate, but the question of sign is a different question from the question of what kind of number it is.
Is 3.0 an integer?
Yes. 3.0 and 3 are two ways of writing one number, and a number cannot change category depending on how it is typed. The same goes for 6/2, which is 3, and for 2.5 + 0.5, which is also 3. Work out the value before deciding what it is.
What is the difference between an integer and a whole number?
In most UK classrooms whole number means 0, 1, 2, 3 and upwards, stopping at zero, while the integers carry on into the negatives. The trouble is that whole number is not used consistently — some books include the negatives. Integer is the word with the settled meaning, which is why exam questions use it.
Is a negative number an integer?
It is, provided it has no fractional part. −8 is an integer; −8.4 is not. This is worth saying plainly because the word integer is often introduced through counting, which leaves some students assuming it must be positive. The list runs in both directions, and the negative half of it is every bit as much part of the set as the positive half.
Fuentes
- Cambridge IGCSE Mathematics (0580) — Cambridge Assessment International Education
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