That’s if you add two of the same odd number. The more general proof is basically the same though: let n and m be integers, then 2n+1 and 2m+1 are odd. (2n+1) + (2m+1) = 2n + 2m + 2 = 2(n+m+1) which will be even.
Or you can just like, understand that an odd number is one more than an even number so if you add them together it’s two more than an even number, hence even.
Which is the layman’s terms of the proof… I don’t get what your goal is.
Is it a building block for learning to read mathematical works? Yes, of course it is.
Is this a ridiculous formalized statement? Yes, of course it is. But that’s the point. We need to practice the trivial to build the scaffolding to tackle the exceptional.
I am not wont to draw conclusions with minimal evidence, but your post seems like you are a malicious reductionist that may be suffering from Dunning Kruger syndrome. I apologize in advance if I have miscategorized you based on this limited sample.
To confirm, you are asserting that the foundation for your answer (mathematical reasoning) does not require any mathematics to understand why it is true.
It’s very dangerous to take a reductionist approach and not be aware of the baked in assumptions you are using. For example, the terms even and odd (for this problem) are well defined as concepts for integers. Which means that your hand-wave statement is true as a result of definitions that were likely created to ensure this property held true.
The notion that “I don’t need math to understand why this is true” is like saying “I made an observation on a phenomenon and I don’t need science to know it’s true.” Which, as you are hopefully aware, is again reductionist and leads to a huge distrust of science from the science illiterate.
I don’t understand what you are trying to say. I just wanted to provide an easier way to reason why it is true, so that people who don’t do math as much as you do could also see the logic behind it. I don’t see how an easy to understand reasoning can be a bad thing?
Quick Proof: Let k be an even number, then (k +1) is odd.
(k +1) + (k+1) = k + 1 + k + 1 = 2k + 2 which will be even.
That’s if you add two of the same odd number. The more general proof is basically the same though: let
nandmbe integers, then2n+1and2m+1are odd.(2n+1) + (2m+1) = 2n + 2m + 2 = 2(n+m+1)which will be even.This is why I failed at uni. I’m struggling so hard to make sense of such proofs, even if I understand the underlying concepts… :(
It helped me to lean on the different principals as an example.
The easiest being Principal of Induction. Substitute
mandnwith 1,3,5,7,9…After going through a few iterations you can see if it holds up enough to keep testing with other principals. (Super simplified).
Or you can just like, understand that an odd number is one more than an even number so if you add them together it’s two more than an even number, hence even.
Definitely, that’s how I’d explain it in words
Which is the layman’s terms of the proof… I don’t get what your goal is.
Is it a building block for learning to read mathematical works? Yes, of course it is. Is this a ridiculous formalized statement? Yes, of course it is. But that’s the point. We need to practice the trivial to build the scaffolding to tackle the exceptional.
I am not wont to draw conclusions with minimal evidence, but your post seems like you are a malicious reductionist that may be suffering from Dunning Kruger syndrome. I apologize in advance if I have miscategorized you based on this limited sample.
Edit: I am never happy with my formatting.
I just wanted to show you don’t need any mathematics to understand why this is true.
The proof is exactly the same though.
never said it isn’t
To confirm, you are asserting that the foundation for your answer (mathematical reasoning) does not require any mathematics to understand why it is true.
It’s very dangerous to take a reductionist approach and not be aware of the baked in assumptions you are using. For example, the terms even and odd (for this problem) are well defined as concepts for integers. Which means that your hand-wave statement is true as a result of definitions that were likely created to ensure this property held true.
The notion that “I don’t need math to understand why this is true” is like saying “I made an observation on a phenomenon and I don’t need science to know it’s true.” Which, as you are hopefully aware, is again reductionist and leads to a huge distrust of science from the science illiterate.
I don’t understand what you are trying to say. I just wanted to provide an easier way to reason why it is true, so that people who don’t do math as much as you do could also see the logic behind it. I don’t see how an easy to understand reasoning can be a bad thing?