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PROOF 79

Prove.

a × 0 = 0

On the integers ℤ.

What you may use

A1a + 0 = a
additive identity
A2(a + b) + c = a + (b + c)
associativity of addition
A3−a with a + (−a) = 0 exists
additive inverse
A4a(b + c) = ab + ac
distributive law
A5ab = ba
commutativity of multiplication
Ea = b ⟹ same operation on both sides
properties of equality

Nothing outside this list may be cited.

Theorem T1

For every a, a × 0 = 0

Proof.

Related labs

Negative Numbers lab →Variables & Expressions lab →

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