The expression "1 + 1" equals 2 rather than 11 because of the fundamental principles of arithmetic. In the decimal number system, which is the one we commonly use, each digit has a place value. In this system, the digit "1" represents the quantity of one, and when we add two of these "1"s together, we are combining two units. This results in the sum of 2, not 11.
The representation of 11 is distinct from 2 because it consists of two digits, each with its own place value. The first digit "1" is in the tens place, and the second "1" is in the ones place. So, when we say "11," we are expressing the quantity of one ten and one one.
In contrast, the expression "1 + 1" involves the addition of two ones, resulting in the simple sum of two units. This is a fundamental principle of arithmetic where the operation of addition combines quantities, and the result depends on the values being added. In this case, adding two ones yields a sum of 2, not 11, as we are not concatenating digits to create a multi-digit number, but rather performing basic addition.
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