why Integer.MAX_VALUE + 1 == Integer.MIN_VALUE?

Question

System.out.println(Integer.MAX_VALUE + 1 == Integer.MIN_VALUE);

is true.

I understand that integer in Java is 32 bit and can\'t go above 2³

Answer 1

Because the integer overflows. When it overflows, the next value is Integer.MIN_VALUE. Relevant JLS

If an integer addition overflows, then the result is the low-order bits of the mathematical sum as represented in some sufficiently large two's-complement format. If overflow occurs, then the sign of the result is not the same as the sign of the mathematical sum of the two operand values.

Answer 2

The same reason why the date changes when you cross the international date line: there's a discontinuity there. It's built into the nature of binary addition.