Proof techniques #1: Proof by Induction.
This technique is used on equations with 'n' in them. Induction
techniques are very popular, even the military use them.
SAMPLE: Proof of induction without proof of induction.
We know it's true for n equal to 1. Now assume that it's true
for every natural number less than n. N is arbitrary, so we can take n
as large as we want. If n is sufficiently large, the case of n+1 is
trivially equivalent, so the only important n are n less than n. We can
take n = n (from above), so it's true for n+1 becuase it's just about n.
QED. (QED translates from the Latin as "So what?")
This technique is used on equations with 'n' in them. Induction
techniques are very popular, even the military use them.
SAMPLE: Proof of induction without proof of induction.
We know it's true for n equal to 1. Now assume that it's true
for every natural number less than n. N is arbitrary, so we can take n
as large as we want. If n is sufficiently large, the case of n+1 is
trivially equivalent, so the only important n are n less than n. We can
take n = n (from above), so it's true for n+1 becuase it's just about n.
QED. (QED translates from the Latin as "So what?")
Related:
- Proof techniques #1: Proof by Induction.
This technique is used on equations with "_n" in them.
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