proven vector
I'm trying to prove a≥a from Analysis I. Is this proof correct / how could it be written better?
Proof.
Let a∈N. We will show a≥a using induction. In the base case, a=0. By def 2.2.1, a = 0 + a. By the commutative property, a = a + 0. By def 2.2.11, a≥a. This proves the base case.
We will now prove the inductive case by showing a++≥a++. By the same logic as the base case, (a++) = 0 + (a++) = (a++) + 0. Because (a++) = (a++) + 0, By def 2.2.11, a++≥a++. This proves the inductive case.
pulsar bear
it is correct but you don't need induction to prove this
proven vector
Thanks 🙂
royal cape
a ∈ N, a ≥ a:
have a = a ∨ a > a from a ≥ a,
have a = a from left a = a ∨ a > a,
show a = a from identity.
QED
I might be misunderstanding what you're saying, but doesn't this beg the question?
pulsar bear
usually ">=" is defined at "equal or >", or like, ">" is defined as ">= but unequal", so that proof would be the usual
but in this case the definition is specific, you need to follow the process of writting that sum for some natural number etc
btw this is from Terence Tao's book, isn't it?
proven vector
usually ">=" is defined at "equal or >", or like, ">" is defined as ">= but uneq...
Ok, that makes sense