Why is Infinity a number?

Question

In JavaScript, isNaN(Infinity) returns false, as if Infinity were a number; but several arithmetic operations on Infinity behave as if it were the mathematical infinity, which is not a number:

So, why doesn't isNaN(Infinity) return true? Is it because its value defaults to a Number object?

Infinity is a number... Also a NaN is a number, it just doesn't equal itself. — John Dvorak, May 31 '16 at 17:17
the IsNaN function merely tests to see if a value is equivalent to the value `NaN`. It's not a check to see if something is not a number. Infinity != NaN. — ManoDestra, May 31 '16 at 17:17
@JanDvorak `typeof NaN === 'number'` but `isNaN(NaN) === true` — Patrick Roberts, May 31 '16 at 17:18
@ManoDestra _Technically_ it's a check to see if said object, _when coerced to a number_, is `NaN`. — Patrick Roberts, May 31 '16 at 17:19
"In mathematics, "infinity" is often treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as natural or real numbers." - https://en.wikipedia.org/wiki/Infinity — ceejayoz, May 31 '16 at 17:27

score 1 · Answer 1 · edited Apr 13 '17 at 12:19

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Infinity is not NaN because you are able to use it in mathematical expressions. Obviously 1 + NaN would never work, but 1 + Infinity returns Infinity (See here). Many of the examples that you have in your link are mathematically indeterminate, which is why they return as Nan. For example, Infinity * 0 is indeterminate (See here).

Hope this helps.

edited Apr 13 '17 at 12:19

Community

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answered May 31 '16 at 17:22

Brian Howell

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Patrick Roberts · Answer 2 · 2016-05-31T17:31:17.550

The reason isNaN(Infinity) returns false has nothing to do with mathematical technicalities, it's simply because its implementation is equal to this:

function isNaN(object) {
  var coerced = +object;

  return coerced !== coerced;
}

In other words, it coerces the input to a Number. If the coerced value is determined to be NaN (by checking if it is not strictly equal to itself), then it returns true. Otherwise it returns false.

[Infinity, null, undefined, true, new Date(), {}, [], [1], [1,2,3], 'blah', '4'].forEach(function (object) {
  console.log('object: ' + (typeof object !== 'number' ? JSON.stringify(object) : object));
  console.log('coerced: ' + (+object));
  console.log('isNaN: ' + isNaN(object));
  console.log('==================');
});

Why is Infinity a number?

2 Answers2