Proof techniques
Okay kiddo, so let's say you want to prove something, like 2 + 2 = 4. There are different ways to prove it, and those ways are called "proof techniques".
One way is called "direct proof". This is when you show step by step how you got to the answer. So, for example, you could say:
- 2 + 2 = 4 because when you add 2 and 2 together, you get a total of 4.
Another way is called "proof by contradiction". This is when you assume the opposite of what you want to prove, and then show that it leads to a contradiction (something that doesn't make sense). So, for example:
- Let's say we want to prove that there are no apples in a basket. We could assume that there is an apple in the basket. Then, we show that this leads to a contradiction because we know for sure that there are no apples in the basket.
Another way is called "proof by induction". This is when you prove something by showing that it works in a specific case, and then show that it works for all cases. For example:
- Let's say we want to prove that the sum of the first n even numbers is n(n+1). We could prove it for the case where n=1 (the sum of the first even number, which is 2, is 1(1+1) = 2). Then, we assume that it works for some arbitrary value of n (let's say n=k), and then show that it also works for n=k+1 (the sum of the first k+1 even numbers is (k+1)(k+2)).
So, those are some ways to prove things, and they're called "proof techniques". Does that make sense, kiddo?
One way is called "direct proof". This is when you show step by step how you got to the answer. So, for example, you could say:
- 2 + 2 = 4 because when you add 2 and 2 together, you get a total of 4.
Another way is called "proof by contradiction". This is when you assume the opposite of what you want to prove, and then show that it leads to a contradiction (something that doesn't make sense). So, for example:
- Let's say we want to prove that there are no apples in a basket. We could assume that there is an apple in the basket. Then, we show that this leads to a contradiction because we know for sure that there are no apples in the basket.
Another way is called "proof by induction". This is when you prove something by showing that it works in a specific case, and then show that it works for all cases. For example:
- Let's say we want to prove that the sum of the first n even numbers is n(n+1). We could prove it for the case where n=1 (the sum of the first even number, which is 2, is 1(1+1) = 2). Then, we assume that it works for some arbitrary value of n (let's say n=k), and then show that it also works for n=k+1 (the sum of the first k+1 even numbers is (k+1)(k+2)).
So, those are some ways to prove things, and they're called "proof techniques". Does that make sense, kiddo?
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