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Formal proofs present the oh-so-mathematical evidence in two columns: one for the statement they are claiming is true, and the other for the reason...
Indirect proofs (or proofs by contradiction) prove their conclusion by showing that the opposite cannot be true. You can use this in math and in ar...
If you already know what a conditional statement is, then you're smarter than you look. And boy do you look smart.
Indirect Proofs 1734 Views
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Description:
Indirect proofs (or proofs by contradiction) prove their conclusion by showing that the opposite cannot be true. You can use this in math and in arguments with your siblings.
Transcript
- 00:03
indirect proofs a la shmoop from one point of view the world is a [Young girl looks through binoculars]
- 00:09
bucket of hypocrite or contradictions green-friendly rock stars begged the
- 00:14
world to donate to the poor and support our environment but fly in to their
- 00:18
concerts on vastly expensive gas guzzling jets we want to be in shape but [Jet lands on runway]
- 00:23
burger and french fry companies pay Olympic athletes to advertise their
Full Transcript
- 00:27
stuff even mathematicians worshippers of logic and reason contradict themselves
- 00:32
from time to time hopefully these contradictions are only
- 00:36
in indirect proofs an indirect proof or proof by contradiction is a type of
- 00:42
argument that proves its conclusion by showing that the opposite cannot be true
- 00:47
talk about meaning around the bush let's say that segments AB and CD are
- 00:53
perpendicular and we're asked to prove that angle ABC is not a straight angle
- 01:00
you see the word not in the conclusion yeah that's a hint that you might want [Light bulb turns on]
- 01:05
to try using an indirect proof first thing we do is take our conclusion and
- 01:10
assume the opposite that it is true so in this case we assume that angle ABC is
- 01:16
a straight angle now let's find that contradiction we'll start with our
- 01:21
assumption that angle ABC is a straight angle straight angles are 180 degrees in [A protractor appears]
- 01:26
measure so the measure of angle ABC is 180 degrees go with us on this now let's
- 01:34
use what we're actually given segments AB and CD are perpendicular to each
- 01:40
other we know that perpendicular segments make
- 01:43
right angles so angle ABC must be a right angle
- 01:47
all right angles are 90 degrees in measure so angle ABC must have a measure
- 01:53
of 90 degrees too... hold on a minute statement 2 says that angle ABC is 180 [Statement 2 highlighted from table]
- 01:59
degrees but statement 5 says it's 90 degrees
- 02:02
there's no way both statements can be true at the same time in our same
- 02:06
dimension so we've contradicted ourselves since we
- 02:10
made an assumption that resulted in a contradiction we know our assumption has
- 02:13
to be false so we can conclude that angle ABC is not a straight angle it may
- 02:20
have been indirect but we finished the job we've fixed our contradiction and [Man and woman arguing and young girl smiles]
- 02:24
done what we set out to do now all that's left is to fix that ozone layer
- 02:28
hopefully sooner than later one [Plaster appears over planet earth]
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