What are some useful tips when it comes to proof basics to keep in mind like odd x odd is always odd or odd x even is always even

I tend to struggle with these when I don’t know some of the basics. If anyone could provide me a list or direct me to where I can find one id really appreciate it.

I tend to struggle with these when I don’t know some of the basics. If anyone could provide me a list or direct me to where I can find one id really appreciate it.

Original post by HIYA8787

What are some useful tips when it comes to proof basics to keep in mind like odd x odd is always odd or odd x even is always even

I tend to struggle with these when I don’t know some of the basics. If anyone could provide me a list or direct me to where I can find one id really appreciate it.

I tend to struggle with these when I don’t know some of the basics. If anyone could provide me a list or direct me to where I can find one id really appreciate it.

I can't provide tips specifically for EdExcel, but for maths proofs at A Level you only have 4 types of worry about for your exam:

https://www.vivaxsolutions.com/maths/alproofs.aspx

•

Disprove a conjecture

•

Proof by exhaustion

•

Proof by deduction

•

Proof by contradiction

Conjecture: find one example that disproves the statement

Exhaustion: list out all possible outcomes based on the rule and either prove or disprove the statement

Deduction: break down the statement, and try to use algebra to deduce why the statement is true or false

Contradiction: assume the opposite of the statement is true, and try to disprove your position to prove the statement is true

It's more about practice more than anything unfortunately. It can take a while to get, but once you do it's usually relatively straightforward.

I think writing proofs is more about structuring your argument in a logical way. Usually A-Level proofs are straightforward.

Let's say you want to prove that "An odd number times another odd number is odd".

Usually before I do anything, I start my first line with

"Let x,y be odd integers. We want to show that xy is also odd."

Yes, you're just re-writing the question again, but it's actually helpful (for me at least) to identity (i) what is the assumption - the "let" part; and (ii) what is our goal - the "we want to show" part.

Then from here, write down the definition of every keywords that needs to be defined. Here it's relatively straightforward, the word "odd" need to be defined. Of course you can go with the definition that "n is odd if 2 doesn't divide n", but you then need to say what "2 divides n" means.

Then it's a case of just try stuff. Now we don't really know at first glance a direct method is sufficient (this should be your first thing to try), or we need "more fancy" tricks like contradiction or induction. But the key is to just try. Usually you don't have much sensible options to go from the definition. If you get stuck, start from your goal (i.e. answer the question "what implies your 'we want to show' bit?"), and hope you can bridge between your assumption and your goal.

But the moral here is pretty simple: Know your definitions.

Let's say you want to prove that "An odd number times another odd number is odd".

Usually before I do anything, I start my first line with

"Let x,y be odd integers. We want to show that xy is also odd."

Yes, you're just re-writing the question again, but it's actually helpful (for me at least) to identity (i) what is the assumption - the "let" part; and (ii) what is our goal - the "we want to show" part.

Then from here, write down the definition of every keywords that needs to be defined. Here it's relatively straightforward, the word "odd" need to be defined. Of course you can go with the definition that "n is odd if 2 doesn't divide n", but you then need to say what "2 divides n" means.

Then it's a case of just try stuff. Now we don't really know at first glance a direct method is sufficient (this should be your first thing to try), or we need "more fancy" tricks like contradiction or induction. But the key is to just try. Usually you don't have much sensible options to go from the definition. If you get stuck, start from your goal (i.e. answer the question "what implies your 'we want to show' bit?"), and hope you can bridge between your assumption and your goal.

But the moral here is pretty simple: Know your definitions.

(edited 2 months ago)

Original post by tonyiptony

I think writing proofs is more about structuring your argument in a logical way. Usually A-Level proofs are straightforward.

Let's say you want to prove that "An odd number times another odd number is odd".

Usually before I do anything, I start my first line with

"Let x,y be odd integers. We want to show that xy is also odd."

Yes, you're just re-writing the question again, but it's actually helpful (for me at least) to identity (i) what is the assumption - the "let" part; and (ii) what is our goal - the "we want to show" part.

Then from here, write down the definition of every keywords that needs to be defined. Here it's relatively straightforward, the word "odd" need to be defined. Of course you can go with the definition that "n is odd if 2 doesn't divide n", but you then need to say what "2 divides n" means.

Then it's a case of just try stuff. Now we don't really know at first glance a direct method is sufficient (this should be your first thing to try), or we need "more fancy" tricks like contradiction or induction. But the key is to just try. Usually you don't have much sensible options to go from the definition. If you get stuck, start from your goal (i.e. answer the question "what implies your 'we want to show' bit?"), and hope you can bridge between your assumption and your goal.

But the moral here is pretty simple: Know your definitions.

Let's say you want to prove that "An odd number times another odd number is odd".

Usually before I do anything, I start my first line with

"Let x,y be odd integers. We want to show that xy is also odd."

Yes, you're just re-writing the question again, but it's actually helpful (for me at least) to identity (i) what is the assumption - the "let" part; and (ii) what is our goal - the "we want to show" part.

Then from here, write down the definition of every keywords that needs to be defined. Here it's relatively straightforward, the word "odd" need to be defined. Of course you can go with the definition that "n is odd if 2 doesn't divide n", but you then need to say what "2 divides n" means.

Then it's a case of just try stuff. Now we don't really know at first glance a direct method is sufficient (this should be your first thing to try), or we need "more fancy" tricks like contradiction or induction. But the key is to just try. Usually you don't have much sensible options to go from the definition. If you get stuck, start from your goal (i.e. answer the question "what implies your 'we want to show' bit?"), and hope you can bridge between your assumption and your goal.

But the moral here is pretty simple: Know your definitions.

Original post by MindMax2000

I can't provide tips specifically for EdExcel, but for maths proofs at A Level you only have 4 types of worry about for your exam:

https://www.vivaxsolutions.com/maths/alproofs.aspx

Conjecture: find one example that disproves the statement

Exhaustion: list out all possible outcomes based on the rule and either prove or disprove the statement

Deduction: break down the statement, and try to use algebra to deduce why the statement is true or false

Contradiction: assume the opposite of the statement is true, and try to disprove your position to prove the statement is true

It's more about practice more than anything unfortunately. It can take a while to get, but once you do it's usually relatively straightforward.

https://www.vivaxsolutions.com/maths/alproofs.aspx

•

Disprove a conjecture

•

Proof by exhaustion

•

Proof by deduction

•

Proof by contradiction

Conjecture: find one example that disproves the statement

Exhaustion: list out all possible outcomes based on the rule and either prove or disprove the statement

Deduction: break down the statement, and try to use algebra to deduce why the statement is true or false

Contradiction: assume the opposite of the statement is true, and try to disprove your position to prove the statement is true

It's more about practice more than anything unfortunately. It can take a while to get, but once you do it's usually relatively straightforward.

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