Due to rounding it won't happen if you keep adding 1, but if you keep increasing $i, even the floating point number will run out of bits; then $i becomes "not a number".

If it's IEEE-754 floating point it should become +Inf...

Ok, not really. At some point the exponent is going to be large enough that you can't represent a +1 difference in the significand, and $i+1 == $i;

# nvtype='double', nvsize=8;
perl -le 'for$ex(0..128){$i=2**$ex;print"$ex $i"and last if$i==$i+1}'
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