Mathematics

12:00 AM

Some people think "n" is not a number.

but then how can n = 3?

To compute, $(a+b)(c+d)$ is first thought of as the product of two elements $a+b$ and $c+d$. Then we look at $a+b$ as a sum and use the distributive property to get $a(c+d)+b(c+d)$ where we are still looking at $c+d$ as an element of the group....

Skullpatrol

@anon Spoonwood???

territory

QED

@Skullpatrol you're ignoring me again

robjohn

Next we look at $c+d$ as a sum of two elements and use the distributive property again to get $ac+ad+bc+bd$.

So we need to look at $a+b$ as an element of the group and also as the sum of two elements of the group.

Skullpatrol

@QED your explanation was clear, but again I'm not able to talk to two or more people at one time sir

robjohn

12:04 AM

I don't know if that relates to what you are trying to do or not

QED

@Skullpatrol, will you stop ignoring me please

Skullpatrol

@QED I will try

but again I'm not able to talk to two or more people at one time sir

@anon Could you please elaborate on "the distinction between the result of an operation and the operation itself expressed in the same way with notation. We've officially hit Spoonwood territory here."

QED

I'm not asking you to

anon

The distinction part or the Doug part?

Skullpatrol

@anon the distinction part

thanks for the link

anon

12:13 AM

See here. The expression $2\times(3\times4)$ evaluates to, or results in, the number $24$, but technically it represents the process of multiplying $3$ times $4$ and then feeding that result into $2\times[]$ and getting the result of that. So on the one hand it represents a number and on the other hand it also represents the operations to get to that number.

Skullpatrol

@anon thanks for referring me to a post with -25 votes ... I think I'll drop the question thanks

@anon So does a + b represent a number or the operation to get that number?

anon

Both.

Skullpatrol

and the same holds true for ab

anon

Mhmm.

Skullpatrol

12:32 AM

@anon So when pre-algebra students are confronted with the statement "we name something in algebra simply by how it looks, such as a + b is called the sum of a and b" We should tell them that this expression, a + b, is both the adding of a and b together and the resulting sum???

anon

I would tell them it can be understood in both those ways, yes. Why, are you supposed to be teaching a pre-algebra class? Or are you taking pre-algebra?

Skullpatrol

Both

anon

Goddamnit. This is a Windows computer and there's no MSPaint on it!

Dylan Moreland

Isn't Paint the reason people use Windows?

anon

I can screencap with Ctrl+PrintScreen and it copies the image to my clipboard. How do I save this as an image using either Gimp or OpenOffice Draw?

Dylan Moreland

12:46 AM

Often there's a "New from Clipboard" option in the File menu. Maybe just make a large new document and hit Paste?

anon

I was thinking about the problem of generalizing the Cauchy-Riemann equations to number fields.

You can't define a derivative directly because limits won't generally exist inside fields that are incomplete, and moreover there is an arbitrary choice of valuation necessary for the definition to make sense. So I was thinking of one possible workaround in particular (Einstein notation used):