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comment Functions which are Continuous, but not Bicontinuous
@julian.marr: that inverse image is open when considered as a subset of the domain.
Aug
30
comment $g\left( x \right)=3-\sqrt { x+3 } $
Do you want to call it $g$ or $y$? Make up your mind!
Aug
28
comment how many spheres can all touch a single one?
@Narasimham: It is true that "equal-sized" is, strictly speaking, ambiguous here: equal to each other, or equal to the original sphere? But it's obvious that the second interpretation is intended.
Aug
27
comment Inequality with Four Numbers
this is almost unreadable why dont you use line breaks and punctuation not to mention latex but at least its correct well done
Aug
27
comment Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142.
As Stefan4024 shows, there must be three people whose ages sum to at least $143$. James claims that there must be three people whose ages sum to at least $144$, but his argument is flawed (see my comment). However, I can't find an example where $143$ is the maximum, so perhaps $144$ is provable. Anybody?
Aug
27
comment Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142.
$4 \times 47 + 3 \times 48 = 332$, so you don't need any 50-year-olds.
Aug
27
comment How many poker hands until statistically significant winner
This is impossible to answer, because it depends heavily on the general skill level. A skilful game will have a much lower variance than a beginners' game.
Aug
26
awarded  Yearling
Aug
25
comment Find the sum of all the number formed by 2,4,6, and 8 without repetition.Number may be of any digit like 2, 24, 684, 4862.
@Timbo: Feel free to post your own answer. This is how I chose to post mine $-$ I think interested readers can work such details out for themselves.
Aug
25
comment can a real number be added to a complex number
@kimm: See what you've started! The point is this: The natural way to define $\mathbb N,\mathbb Z,\mathbb Q,\mathbb R,\mathbb C$ is as a sequence of ever more sophisticated constructions, wherein each member of the sequence has a canonical embedding into its successor. In this view, $\mathbb R$ is not a subfield of $\mathbb C$. But once you have done all this, it just becomes convenient to treat the various members as if they were all subfields or subrings of $\mathbb C$. This is a kludge, if you like, but it can always be justified when required.
Aug
25
comment can a real number be added to a complex number
@AsafKaragila: And $\mathbb H$. And $\mathbb O$. The trouble with that approach is that you need to know where you're going to end up before you start $-$ if you're ever going to be using octonions, then you'd better define $\mathbb N$ as a subset of $\mathbb O$, hadn't you?
Aug
25
comment can a real number be added to a complex number
@AsafKaragila: I have never seen that approach, so thanks for the info. It doesn't get us to $\mathbb C$, though!
Aug
25
comment can a real number be added to a complex number
@PatrickStevens: Thank you!
Aug
25
comment can a real number be added to a complex number
@LeeMosher: There is a difference between seeing things that way and defining them that way.
Aug
25
comment can a real number be added to a complex number
@Daniel: Well, exactly.
Aug
25
comment can a real number be added to a complex number
@DanielFischer: Yes, but nobody does it that way, surely?
Aug
25
comment can a real number be added to a complex number
You have covered my objection nicely in your third paragraph. (But then you go on to say that the reals "form a subfield" of the complexes. And we're back to square one!)
Aug
25
comment can a real number be added to a complex number
I think the question is a bot more nuanced than you give it credit for. A real number is not the same as its image under the inclusion map. I would say the inclusion map allows you to map any real number to a complex number (in a canonical way).
Aug
25
comment Combined pulling power of multiple engines in a train
The first engine is not pulling the second engine along; the second engine is quite capable of pulling itself along.
Aug
25
awarded  Nice Answer