Prove the following
prove0!=1
Let n be a whole number
where n! represents:
The product of n and all integers below it through 1.
The factorial formula for n is
n! = n · (n - 1) · (n - 2) · ... · 3 · 2 · 1
Written in partially expanded form, n! is:
n! = n · (n - 1)!
Substitute n = 1 into this expression:
n! = n · (n - 1)!
1! = 1 · (1 - 1)!
1! = 1 · (0)!
For the expression to be true, 0! must equal 1.
Otherwise, 1!≠1 which contradicts the equation above
Final Answer
0! = 1
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Build a bridge using corollaries, axioms, and theorems to get to the declarative statement.
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- axiom
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- proof
- an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion
- theorem
- A statement provable using logic
