What is the Smallest Integer with Two Different Digits?

The question often arises in discussions about number theory and digital manipulation: what is the smallest integer with two different digits?

The initial consensus seems to be 10, which is composed of the digits 1 and 0. However, the context in which the term 'integer' is used can significantly influence the answer. Let's explore the nuances.

10 - The Small Integer with Two Different Digits?

Many argue that 10 is the smallest integer with two different digits, reasoning that it meets the criteria cleanly with the digits 1 and 0. However, this conclusion is based on the assumption that the question is asking for a non-negative integer (an unsigned integer).

-98 or 10: Which is the Correct Smallest Integer?

One perspective challenges this by suggesting that the answer should include signed integers. Here, -98 emerges as the smallest two-digit integer with distinct digits, as the question does not explicitly exclude them. Some argue that the integer must be a whole number, excluding fractions, but that it can be signed. Thus, -98 is the smallest negative integer with two different digits.

It is important to note that the answer may also depend on whether the sign itself is considered a digit. If the sign is not included as a digit, then 10 remains the smallest unsigned integer with two different digits. However, if the sign is considered, then -98 takes the lead as the smallest signed integer with two different digits.

Conclusion and Further Considerations

The debate highlights the importance of precise wording in mathematical questions. In some contexts, the smallest integer with two different digits could be 10, and in others, it could be -98. The inclusion of negative numbers, the consideration of the sign as a digit, and the definition of integers all play crucial roles.

Mathematics is a field rich in such nuanced and thought-provoking debates, encouraging a deeper exploration of fundamental concepts and their applications.

Keywords: smallest integer, different digits, negative integer, positive integer