The smallest integer is 0.
Step 1: Integers include negative numbers, zero, and positive numbers.
\(-3,\,-2,\,-1,\,0,\,1,\,2,\,3,\,\ldots\)
Step 2: A number is smaller if it is to the left on the number line.
Step 3: There is a number smaller than 0.
\(-1 < 0\)
Step 4: There is always another smaller integer.
\(-2 < -1\)
\(-3 < -2\)
\(\ldots\) continues without end to the left.
Conclusion: No smallest integer exists. Therefore, the statement “The smallest integer is 0” is false.