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#26 Re: Dark Discussions at Cafe Infinity » Did you know? » 2019-05-17 13:46:09
#21. Did you know?
Shai Wosner is an Israeli-born pianist.
I have just enjoyed listening to him playing Franz Schubert’s Piano Sonata in A major, D. 959, on BBC Radio 3.
#28 Re: Introductions » Winter Lover » 2019-05-17 12:18:11
Salut, John! Bon retour!
(Hi John! Welcome back!)
#29 Re: Help Me ! » logic » 2019-05-17 11:52:38
I would use:
[list=*]
[*]Hxy : x hides y in public,
hxy : x has y,
Mx : x is modest,
a : Angus,
p : private bits.[/*]
[/list]
Then the premises are:
[list=*]
[*]∀x((Mx∧hxp)→Hxp),
∀y(hay→¬Hay).[/*]
[/list]
The first premise is equivalent to
•∀x(¬Hxp→¬(Mx∧hxp)) ≡ ∀x(¬Hxp→(¬Mx∨¬hxp)).
Substituting x = a into it gives
•¬Hap→(¬Ma∨¬hap).
Substituing y = p into the second premise gives
•hap→¬Hap.
It follows that
•hap→(¬Ma∨¬hap) ≡ ¬hap∨(¬Ma∨¬hap) ≡ ¬Ma∨¬hap
which is the conclusion. Therefore the argument is valid.
#30 Re: Help Me ! » Find the order of the cyclic subgroup of D2n generated by r » 2019-05-17 10:17:13
Does it implies that the order of cyclic subgroup {1, r, r^2, ... , r^n-1} of D2n is n then?
Yes.
#31 Re: Help Me ! » Boundary points » 2019-05-17 08:04:02
Try
[list=*]
[*]
[/list]
Then
[list=*]
[*]
[/list]
and
[list=*]
[*]
[/list]
so
[list=*]
[*]
[/list]
#32 Re: Help Me ! » proof of same cardinality » 2019-05-17 02:33:16
Note that
[list=*]
[*]
[/list]
is a partition of A since f is surjective and (as a bona fide function) is well defined. So, use the axiom of choice to pick for each b ∈ B exactly one aᵇ ∈ f⁻¹(b). This will give you an injection
[list=*]
[*]
[/list]
#33 Re: Help Me ! » Intergration Problem Please Help » 2019-05-17 01:27:27
If you shift the curve 2 units to the right, you’ll be rotating the curve y = √(4−[x−2]) around the y-axis instead.
#34 Re: Jokes » (7^2 + 2^1 + 1^1 + 1^1) One Liners » 2019-05-17 00:16:31
Why is this thread called “(7^2 + 2^1 + 1^1 + 1^1)”? 
#35 Re: Dark Discussions at Cafe Infinity » Did you know? » 2019-05-16 23:30:37
#19. Did you know?
#18 comes between #17 and #19.
#36 Re: Help Me ! » screws - modular arithmetic » 2019-05-16 13:25:57
#37 Re: Help Me ! » Real Analysis Proof for Infimum and Supremum of functions » 2019-05-16 10:18:10
That proves (1) and (4). The others are a tad trickier.
And
#39 Re: Help Me ! » Euler Characteristic - is it true that... » 2019-05-16 05:21:16
By “could be turned into each other by the right set of manipulations”, do you mean homeomorphic?
In that case, the answer is no. It is true that two homeomorphic spaces must have the same Euler characteristic, but the converse is not true: it is possible for two non-homeomorphic spaces to have the same Euler characteristic. An example (or two) is the torus and the Klein bottle: both have Euler characteristic 0, but they are not homeomorphic.
#40 Re: Help Me ! » Proof: integer solutions of a polynomial » 2019-05-16 01:31:01
We can write
[list=*]
[*]
[/list]
where g(x) is a polynomial with integer coefficients. If there were an integer solution, say f(n) = 0, then
[list=*]
[*]
[/list] since they are all integers. But if a, b, c are distinct, then so are (n−a), (n−b), (n−c). This is a contradiction because (n−a), (n−b), (n−c) cannot take three distinct values if they can only be ±1.
Thus f(x) = 0 cannot have an integer solution.
#41 Re: Dark Discussions at Cafe Infinity » Did you know? » 2019-05-15 23:41:41
#16. Did you know?
Amebelodon is a genus of extinct proboscidean belonging to Amebelodontidae (the so-called shovel-tuskers), a group of proboscideans related to the modern elephants and their close relative the mammoth.
I read about this a moment ago in the chapter “When the World began” of Dean’s Tell Me the Answer (which misspells the name as “Amebolodon”).
#42 Re: Maths Is Fun - Suggestions and Comments » Minor Upgrade - may or may not go smoothly » 2019-05-15 23:23:45
Given that bobbym is a mathematical god, maybe that's as it should be. Enlightenment requires some effort.
I want to be the second mathematician to go to nirvana! 
#43 Re: Dark Discussions at Cafe Infinity » Did you know? » 2019-05-15 23:09:13
#14. Did you know?
The lari is the unit of currency of Georgia.
I’ve already mentioned it here – but I’m mentioning it again because this came up in the pub quiz I went to on Tuesday! And I knew the answer!
#44 Re: Help Me ! » Six Segments » 2019-05-15 09:38:07
#45 Re: Help Me ! » Word Problem » 2019-05-15 05:30:10
[list=*]
[*]
[/list]
#46 Re: Dark Discussions at Cafe Infinity » icelandic dictionary » 2019-05-15 04:37:08
Ég er að drekka kaffi.
(I’m drinking coffee.)
#47 Re: Dark Discussions at Cafe Infinity » Realism vs Idealism » 2019-05-15 04:33:57
I’m a realistic idealist.
#48 Re: Dark Discussions at Cafe Infinity » What worldy occurrences can we think of in terms of mathematics? » 2019-05-15 04:32:21
One application of mathematics is in Western music. The technique of equal-temperament tuning is based on the 12th root of 2, while the circle of fifths is based on the cyclic group of order 12.
#49 Re: Dark Discussions at Cafe Infinity » Song of the Day! » 2019-05-15 04:10:41
The Last Rose Of Summer
’Tis the last rose of summer,
Left blooming alone;
All her lovely companions
Are faded and gone;
No flower of her kindred,
No rosebud is nigh,
To reflect back her blushes,
And give sigh for sigh.I’ll not leave thee, thou lone one!
To pine on the stem;
Since the lovely are sleeping,
Go, sleep thou with them.
Thus kindly I scatter,
Thy leaves o’er the bed,
Where thy mates of the garden
Lie scentless and dead.So soon may I follow,
When friendships decay,
And from Love's shining circle
The gems drop away.
When true hearts lie withered,
And fond ones are flown,
Oh! who would inhabit
This bleak world alone?
#50 Re: Dark Discussions at Cafe Infinity » Haiku 2 » 2019-05-15 02:46:35
Life must be treasured:
It’s most precious. That’s why I
Resurrect old threads.