Answer:
[tex]2[/tex]
Step-by-step explanation:
[tex]1 + 1 = 2[/tex]
The mathematical proof that 1 + 1 = 2 can be demonstrated using various methods, such as using the Peano axioms or natural numbers. Here is a simple proof using the Peano axioms:
- Axiom 1 (0 is a natural number): This states that there exists a natural number, usually denoted as 0.
- Axiom 2 (Successor function): For every natural number n, there exists a successor number, denoted as S(n), such that S(n) is also a natural number.
- Axiom 3 (No repetition): There are no two distinct natural numbers with the same successor.
- Axiom 4 (Induction): If a statement holds for 0 and it holds for the successor of any number it holds for, then it holds for all natural numbers.
Using these axioms, we can prove that 1 + 1 = 2 as follows:
- We know that 0 + S(0) = S(0), which by definition is equal to 1.
- Applying the successor function to both sides, we get S(0) + S(0) = S(1).
- By the definition of addition, we can rewrite the equation as 1 + 1 = S(0), which by definition is equal to 2.
Therefore, we have proven that 1 + 1 = 2 using the Peano axioms.
