Limits

Unlike in math, where numbers can be arbitrarily big or small, a Java int is "fixed width."

Say you had a piece of paper that was only big enough to write two numbers on.

The only numbers you could write in a base ten system would be those from 0 to 99. You could not write 100 or anything larger.

A Java int is similar except instead of only being able to write 0 to 99 on a piece of paper, a variable that has the type int can represent numbers from -2³¹ to 2³¹ - 1.

If you try to directly write out a number that is outside of that range, Java will not let you.

void main() {
// This will not run
int tooBig = 999999999999;
}

If you do math that should produce a larger number than is representable, the value will "loop around."

void main() {
// This is the value of 2^31 - 1
int atLimit = 2147483647;
// The value will "loop around" to -2^31
int beyondLimit = atLimit + 1;
// This will output -2147483648
IO.println(beyondLimit);
}

When a value loops around because it got too big we call that "overflow." When it loops around because it got too small we call that "underflow."

There are other types which can represent a larger range of integers, as well as types which do not have any limits, but for now int is the only one you will need.