You cannot represent infinity or NAN using an int.
From JLS
The result of a floating-point division is determined by the rules of
IEEE 754 arithmetic:
Division of a nonzero finite value by a zero results in a signed
infinity. The sign is determined by the rule stated above.
Check the IEEE explanation
Why doesn't division by zero (or overflow, or underflow) stop the
program or trigger an error? Why does a standard on numbers include
"not-a-number" (NaN)? The 754 model encourages robust programs. It is
intended not only for numerical analysts but also for spreadsheet
users, database systems, or even coffee pots. The propagation rules
for NaNs and infinities allow inconsequential exceptions to vanish.
Similarly, gradual underflow maintains error properties over a
precision's range.
When exceptional situations need attention, they can be examined
immediately via traps or at a convenient time via status flags. Traps
can be used to stop a program, but unrecoverable situations are
extremely rare. Simply stopping a program is not an option for
embedded systems or network agents. More often, traps log diagnostic
information or substitute valid results.
Flags offer both predictable control flow and speed. Their use
requires the programmer be aware of exceptional conditions, but flag
stickiness allows programmers to delay handling exceptional conditions
until necessary.