Notation

When I answer "show that" questions, I tend to put [Q.E.D] at the end, when I answer normal questions, I use the triangle with 3 dots that represents "therefore" and I also use the "implies that" arrow.

I was just wondering if the people marking our papers, who have bachelors and masters degrees in maths, think that the questions are too easy to warrant the notation,

Having just read through what I've written, I can see my logic is hard to understand.

I imagine the examiners would look at my working and see my notation, the same why I look at this:

1+X=2 => 2-X=1

It just seems like there is no point in using the arrow.

(I'm aware of the fact that the notation is correct, I just feel pretentious using it)

Reply 1

Jkn

11

Original post by Liamnut

I imagine the examiners would look at my working and see my notation, the same why I look at this:

1+X=2 => 2-X=1

It just seems like there is no point in using the arrow.

(I'm aware of the fact that the notation is correct, I just feel pretentious using it)

Why is this at all strange? It is correct, so why are you apprehensive to use it? I personally (and I have always assumed that everyone else I know my age does) use the arrows to join together every line of maths I do, and tend to type it up in solutions as well. In some exams you would lose marks for not using it if it means that something is unclear (not A-levels!)

Perhaps writing 'QED' is a little pretentious and I know people that dislike it (I personally prefer writing a square at the end or writing

\Rightarrow \square

to convey that the proof is complete :biggrin:

) but the logical arrows and therefore dots are not even slightly pretentious.

It's just like if you were in primary school and your class hadn't learnt the full stop yet (but you had been told!) Obviously the rest of your class would be writing sentences with no punctuation, but they would only be asked to write sentences whereby the meaning would be clear even without the full stop. If your teacher sets you an essay, should you include the full stop or shouldn't you? The bottom line is that, so long as you find it so effortless to use, go for it as you will be getting in to good habits for the future.

Btw, for the above example, it is more complete to say that

1+x=2 \iff 2-x=1

What I tend to do is to only include the double arrow when I specifically require both the necessary and sufficient condition. Otherwise, I just use the single arrow regardless :tongue:

Reply 2

Hedgeman49

17

Original post by Liamnut

When I answer "show that" questions, I tend to put [Q.E.D] at the end, when I answer normal questions, I use the triangle with 3 dots that represents "therefore" and I also use the "implies that" arrow.

I was just wondering if the people marking our papers, who have bachelors and masters degrees in maths, think that the questions are too easy to warrant the notation,

Having just read through what I've written, I can see my logic is hard to understand.

I imagine the examiners would look at my working and see my notation, the same why I look at this:

1+X=2 => 2-X=1

It just seems like there is no point in using the arrow.

(I'm aware of the fact that the notation is correct, I just feel pretentious using it)

Just make sure that you actually mean what you write. There is a propensity for A-level and early degree students to misuse the notation, such as using therefore when they mean implies that or only using one direction of implication when both hold.

Reply 3

Jkn

11

Original post by Hedgeman49

..only using one direction of implication when both hold.

Surely you use it as required though? :tongue:

Like:

x=1 \Rightarrow x^2=1 \Rightarrow (x+1)(x-1)=0

seems somewhat more pleasing than

x=1 \Rightarrow x^2=1 \iff (x+1)(x-1)=0

(as both directions is not desirable as the chain of reasoning cannot follow from right to left)? :smile:

Reply 4

Hedgeman49

17

Original post by Jkn

Surely you use it as required though? :tongue:

Like:

x=1 \Rightarrow x^2=1 \Rightarrow (x+1)(x-1)=0

seems somewhat more pleasing than

x=1 \Rightarrow x^2=1 \iff (x+1)(x-1)=0

(as both directions is not desirable as the chain of reasoning cannot follow from right to left)? :smile:

I got pinged by numerous tutors and lecturers for doing it until I eventually bent to their will :tongue:

Reply 5

brianeverit

9

Original post by Liamnut

When I answer "show that" questions, I tend to put [Q.E.D] at the end, when I answer normal questions, I use the triangle with 3 dots that represents "therefore" and I also use the "implies that" arrow.

I was just wondering if the people marking our papers, who have bachelors and masters degrees in maths, think that the questions are too easy to warrant the notation,

Having just read through what I've written, I can see my logic is hard to understand.

I imagine the examiners would look at my working and see my notation, the same why I look at this:

1+X=2 => 2-X=1

It just seems like there is no point in using the arrow.

(I'm aware of the fact that the notation is correct, I just feel pretentious using it)

I always tell my pupils to look carefully at their solution when they have finished it and to ask themselves the question "If someone looks at my solution, could they understand exact;y what I have done?" and if you have to answer no, then it is not a satisfactory solution.

Notation

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