The local marketplace has sold a "math" sparknotes

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296KB, 500x375px

>>8132108

>>8132108
Is the error in the picture or the text? The picture is correct, that's the conventional arrangement of those sets.

>>8132108
I would complain about the definition or rationals not being incredibly clear that improper fractions are redundant, and q should be natural rather than integer. I have some other nitpicks but was unable to identify something major.

Useless comment on hint: I agree that the distinction between whole and natural is useful, but I hate the term "whole" used to add zero, I feel it's misleading.

it seems sketchy to me to say that reals are a set of the complex numbers - they're a construction formed from reals and imaginaries, but not properly a containing set imo

also
>0 not a natural
lol

>>8132108
set of real and imaginary numbers have no common element -> wrong, 0 is in both.

>>8132157
0 isn't a natural number. That's the difference between natural and whole numbers.
>>8132158
How are you supposed to represent that on this kind of chart? And to be quite honest, if you interpret imaginary numbers to be numbers whose squares are nonnegative, zero isn't included. 0i is semantically wrong, but 0 + 0i isn't.

>>8132194
>How are you supposed to represent that on this kind of chart?
No he's right, it's not the chart, it says in the text:
>the sets of real numbers and imaginary numbers have no elements in common and are therefore disjoint sets

>>8132158
Ding-ding-ding! CORRECT! This is the major factual error in the graphic (in the text, near bottom left), and they've been printing it this same way for maybe 15 years.

The error is repeated somewhat in the crude graphic at right; the graphic agian suggests to us that the reals and imaginaries are disjoint within the complexes, which is of course false as has been observed.

Moreover, since the rationals and irrationals together are precisely all of hte reals, the graphical representation of a "real-number-space" outside these two sets is also misleading, unless one were to specify that that space (subset) is empty.

Also the blurb defining the rationals with a bit of context needs polishing. we are to consider "fractions", but the blurb should emphasize /again/, in the later example-text, that the "fractions" are always to consist of integers, etc (and not, as SMBC adroitly reminds us in opposite context, of expressions such as "π/1", which of course is a /fraction/."

>>8132194
in the text, it's explicitely mentionned that reals and imaginaries don't cross.

>if you interpret imaginary numbers to be numbers whose squares are nonnegative
I don't, and no one does.

>>8132108
>i is the number whose square is -1¨

but -i also works.

>>8132204
>(-i)^2 = (-sqrt(1))^2 = -sqrt(1) * -sqrt(1) = sqrt(1)^2 = 1

>>8132210
> i = sqrt(1)
o i am laffin

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>>8132194

It's a good question. Pic related is my sketch of what to do.

Basically you have to represent that 0 belongs to most of these particular sets, but not to all of them. It occurred to me while sketching this that I don't know the detailed differences between a venn diagram and an euler diagram.

>>8132235
You forgot to add the sets of transcendental (non-algebraic) numbers, computable numbers, and the definable real numbers.

These are all non-trivial

>>8132247

It's possible you're having a very dry sense of humor, or else that you're serious. Either way, I anticipated that someone would bring up normals, algebraics, (why not odds and evens while we're at it?), etc. Obviously, we can continue ad infinitum in this wise, once we admit that "everything" is in some sense interesting.

So let me clarify. the object of the exercise has not been to diagram every interesting subset of the complexes, but rather to simply reinterpret the OP's (that is, the chart's) particular diagram as a more accurate and less misleading chart.

>>8132194
Many modern definitions of the natural numbers do actually include 0.

>>8132443
Though, again, I find "whole" and "natural" misleading names, it is still useful to have a single word to describe [math]\mathbb{Z}^+ \setminus \{0\}[/math], as it is used often.

>>8132108
the big mistake appears to be in the rationals, it fails to establish an equivalence class where a/b = p/q iff aq=bp, otherwise 1/2 and 2/4 are distinct numbers

>>8132487
plz read thread to avoid saying something that has already been said