Symbols

bossk171 · 2007-10-30 03:42:53

My math background is High school Calculus, and everything that comes before it, and I love math. I've been hanging out on these boards for a while now and I have a question that's really been bothering me...

I'm really getting hung up on notation. Before being on these boards, I'd never seen "∴" used anywhere. By clicking on the Latex code I figured out it means "Therefore." But What is the difference between "∴" and "⇒" i.e. when do I use one and not the other?

What are some other notations? Is there a symbol for "if" I'm pretty sure the symbols for "and" and "or" are shapes something like"U"s. What does " " mean? Is there a difference between American notation and British notation? Australian Notation? Canadian Notation? For example, I was taught to use "ln" for natural log, but books I read by British authors use "log" (which I use for log base 10).

This is quite frustrating for me, and it must seem like a really dumb question to most of you, but can someone help me out with this? Or at least send me a half way decent link? Thanks.

luca-deltodesco · 2007-10-30 03:50:51

the second symbol ⇒ technically means 'implies' and

means 'if and only if'

so implies, a ⇒ b, if a is true, b must be true, but the converse is not necessarigly true, if a is false, b does not have to be false
if and only if means they are the same, if a is true, b must be true, if a is false, b must be false

ive never used log for ln before, what might happen is that youll be told the base of the logarithm, and then they will use log, and if its not mentioned, you are to assume (depending on the situation) that its base 10

means multiplication (and for vectors, the scalar multiplication -> dot product)
× means multiplication aswell for numbers, and for vectors it means the cross product/vector product

Ricky · 2007-10-30 04:04:35

Symbols will come to you as you learn more math. There is no need to go out and learn them. But they are cool, and I understand the want to. That being said:

But What is the difference between "∴" and "⇒" i.e. when do I use one and not the other?

Therefore is a conclusion. Since n is even, n = 2k, so n*n = 2k*2k = 4k^2 = 2(2k^2). Therefore, n^2 is even. On the other hand, ⇒ is an implication. n even ⇒ n^2 is even. Now here comes the confusion. You can say "n even therefore n^2 is even". But the difference usually lies in "therefore" needs no more argument, while implication is a statement you have or intend to give more justification for. Typically, n even implies n^2 even needs no more justification (it's obvious), so therefore is ok to use. On the other hand, n is a squarefree integer implies the square root of n is irrational needs much more justification, so therefore would not be ok to use.

Is there a symbol for "if" I'm pretty sure the symbols for "and" and "or" are shapes something like"U"s.

There isn't a symbol for "if" because whenever you use "then", you must use "if". So "a ⇒ b" means "If a then b". And is typically ^ and or is v

Is there a difference between American notation and British notation? Australian Notation? Canadian Notation?

I don't know of any major differences, but there are many differences from mathematician to mathematician, let alone country to country. One which seems to be very debatable is how to represent "such that" in set theory. For example, we could say: A = {x in B : x in C} The ":" is translated as "such that". Or on the other hand, A = {x in B | x in C}. I'm in the ":" camp myself.

For example, I was taught to use "ln" for natural log, but books I read by British authors use "log" (which I use for log base 10).

If you're a computer scientist, log is base 2. Engineer, it's base 10, and mathematician is base e.

Here is a link to a pretty decent collection, although by no means complete.

Jai Ganesh · 2007-10-30 04:27:47

Although many symbols are the same always, sometimes you cannot take some of them for granted. log isn't universally log to the base 10, ands neither is ln the natural logarithm.
But there are some symbols in mathematics which are accepted worldwide.
Like a^b is a raised to the power b.
I found it quite difficult to learn what a^^b meant. Later, after surfing the net for the up arrow notation (Knuth's up arrow notation), I learnt there was a symbol for iterations. Then the chained arrow notation of John Conway is much more difficult to comprehend. a->->c->d is too difficult to understand, even after spending a lot of time on the chained arrow notation. The polygon notations (Moser) are difficult too.
a*b is the product of a and b, so on.
Sometimes, the context the symbol is used is also important.
a||b can denote line a is parallel to line b. But there may be other meanings too. (I just checked Ricky's link, thank God, I am right)

Ricky · 2007-10-30 05:36:45

But there are some symbols in mathematics which are accepted worldwide.
Like a^b is a raised to the power b.

Unless your mathematics is involved with computer science, in which case a^b means a XOR b.

mathsyperson · 2007-10-30 07:05:30

I've been taught that ^ is also an alternative symbol instead of x, when referring to the vector cross product.

bossk171 · 2007-10-31 02:29:39

Thanks everyone.

Ricky, your log explanation was particularly helpful, I guess it makes sense to just look at the context.

Math Is Fun Forum

#1 2007-10-30 03:42:53

Symbols

#2 2007-10-30 03:50:51

Re: Symbols

#3 2007-10-30 04:04:35

Re: Symbols

#4 2007-10-30 04:27:47

Re: Symbols

#5 2007-10-30 05:36:45

Re: Symbols

#6 2007-10-30 07:05:30

Re: Symbols

#7 2007-10-31 02:29:39

Re: Symbols

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