but where did the "=3a" come from? Wheeere did "a" come from?. I've seen at least 20 videos on this and I still can't understand it, I feel like I need a back story before I can understand proofs by induction. can you email me an explanation of proof by induction in the simplest of english and a reason for doing each step, or is that asking too much?
+Whilli Whonka So in the statement we are trying to prove, it says "4^(n-1) is divisible by 3". To be divisible by 3 means that you are a multiple of 3. For instance, 12 is divisible by 3 since 3x4 = 12. But in this case, we dont know the exact value of 4^(n-1). We only know it is a multiple of 3 (since it is divisible by 3). So we know 4^(n-1) = 3 x (something), but we dont know if that something is 4 (like with 12) or whatever. So, we use a to represent this whole number. By writing 4^(n-1) = 3a , we are saying that we know 4^(n-1) is a multiple of 3. It is 3 x a, for whatever a is. Hope this helps!
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Just saved my butt, thanks
Helped me so much, thanks!
+Neil Christensen Awesome! Glad to hear it.
but where did the "=3a" come from? Wheeere did "a" come from?. I've seen at least 20 videos on this and I still can't understand it, I feel like I need a back story before I can understand proofs by induction. can you email me an explanation of proof by induction in the simplest of english and a reason for doing each step, or is that asking too much?
+Whilli Whonka So in the statement we are trying to prove, it says "4^(n-1) is divisible by 3". To be divisible by 3 means that you are a multiple of 3. For instance, 12 is divisible by 3 since 3x4 = 12. But in this case, we dont know the exact value of 4^(n-1). We only know it is a multiple of 3 (since it is divisible by 3). So we know 4^(n-1) = 3 x (something), but we dont know if that something is 4 (like with 12) or whatever. So, we use a to represent this whole number. By writing 4^(n-1) = 3a , we are saying that we know 4^(n-1) is a multiple of 3. It is 3 x a, for whatever a is.
Hope this helps!
It did somewhat, i guess it makes sense when I don't think too hard about it
You kinda sound like Elen DeGeneres.