Dmitri Pavlutin
I help developers understand JavaScript and React

Why Math.max() Without Arguments Returns -Infinity

Math.max() is a built-in JavaScript utility function that determines the maximum number from the arguments.

For example, let’s determine the maximum of the numbers 1, 2 and 3:

javascript
Math.max(1, 2, 3); // => 3

As expected, 3 is the maximum of 1, 2, and 3.

What would happen if Math.max() is invoked with just one argument:

javascript
Math.max(1); // => 1

As expected, the maximum of one number is the number itself.

But what would happen if you invoke Math.max() without arguments at all?

javascript
Math.max(); // => -Infinity

While it might be unexpected at first, but calling Math.max() without arguments returns -Infinity. Let’s find out why it happens, and why it’s important to happen this way.

1. Max of one array

Before diving into the main question (why Math.max() without args returns -Infinity), let’s see how Math.max() can be used to determine the maximum number from an array.

Math.max(num1, num2, ..., numN) accepts multiple number arguments and returns the maximum number of them. Simple as a pie.

If you want to determine the maximum number of an array, then you can use the spread arguments operator on the array:

javascript
const numbers1 = [1, 2, 3];
Math.max(...numbers1); // => 3

Math.max(...numbers1) expression uses the spread syntax and returns the maximum number of numbers1 array: 3.

2. Max of 2 arrays

Now let’s try something more interesting. Given two arrays of numbers, let’s determine the maximum number of each array, and then determine the maximum of these 2 maximum values.

A bit overwhelming, but bear with me…

javascript
const numbers1 = [1, 2, 3];
const numbers2 = [0, 6];
const max1 = Math.max(...numbers1);
const max2 = Math.max(...numbers2);
max1; // 3
max2; // 6
Math.max(max1, max2); // => 6

The maximum number of [1, 2, 3] is 3, and of [0, 6] is corresponding 6. The max value from 3 and 6 is 6.

That’s expected.

What about trying to determine the maximum of arrays if one array is empty? Let’s make numbers1 an empty array and try again:

javascript
const numbers1 = [];
const numbers2 = [0, 6];
const max1 = Math.max(...numbers1);
const max2 = Math.max(...numbers2);
max1; // -Infinity
max2; // 6
Math.max(max1, max2); // => 6

Now, having the first array empty, the above code snippet correctly determines 6 as being the maximum of 2 arrays.

What’s interesting is what value returns Math.max(...numbers1): being that numbers1 array is empty, this is the same as calling Math.max() without arguments. Correspondingly, this is -Infinity.

Then Math.max(max1, max2) is evaluated as Math.max(-Infinity, 6), which results in 6.

Now it’s clear why Math.max() returns -Infinity when called without arguments: it’s a way for the max function to be defined upon an empty set.

Making a parallel between max and addition, -Infinity for max is the same as 0 for addition.

The same behavior happens with Math.min() — it returns Infinity when called without arguments.

-Infinity, in regards to the max operation on the real numbers, is called the Identity element.

3. Conclusion

Math.max() called without arguments returns -Infinity to correctly handle the cases multiple maximum operations are performed (max of max of max…), particularly being useful when determining the max value of an empty array.

In simple words, if you’re determining the maximum numbers of 2 arrays, and then determine the maximum of these maximums too, you would get the expected result.

javascript
Math.max(
Math.max(...[]), // -Infinity
Math.max(...[0, 6]) // 6
); // => 6

Challenge: Can you write a sum(num1, num2, ..., numN) function that works exactly like Math.max(), only that it summarizes its argument? What would be the identity element? Share your solution in a comment below!

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About Dmitri Pavlutin

Software developer, tech writer and coach. My daily routine consists of (but not limited to) drinking coffee, coding, writing, coaching, overcoming boredom 😉.
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