Final answer:
Conventional mathematics strictly adheres to the principle that 1 + 1 equals 2 due to the set rules of arithmetic, such as the commutativity of addition, and does not allow for a result of 3.
Step-by-step explanation:
To prove the statement that 1 + 1 can equal 3 is challenging because, within conventional mathematics, this statement is incorrect. The principle of commutativity, shown as A + B = B + A, simply implies that the order of addition does not change the result. Supporting this, addition of real numbers is governed by established mathematical rules and does not allow for 1 + 1 to equal anything other than 2.
Let's consider the given equation A.5 1 + 3 = 1; 2 1 3 3 1 1 < = 4 4' 4 2 3. The first two parts are meant to simplify fractions. Any fraction with the same numerator and denominator equals 1, hence the correctness of these statements within the realm of mathematics. Intuition and commonly accepted definitions also support the claim that 1 + 1 could not equal 3 for counting numbers.
In every intended application, whether by a peasant counting goats or a professor counting students, 12 + 19 must equal 31 not 32, as agreed upon by the rules of arithmetic across cultures and eras. This principle also applies to the addition of simpler numbers like 1 + 1. Therefore, in a typical mathematical sense, 1 + 1 cannot equal 3.