Home | Community | Message Board
You are not signed in.
Sign In New Account
Forum Index Search Posts Trusted Vendors Highlights Galleries FAQ User List Chat Store Random Growery

PlanetSpores.ca
This site includes paid links. Please support our sponsors.

Community > The Pub
Threaded Mode Threaded  Previous topic Previous  View all topics Index  Next topic Next 

Welcome to the Shroomery Message Board! You are experiencing a small sample of what the site has to offer. Please login or register to post messages and view our exclusive members-only content. You'll gain access to additional forums, file attachments, board customizations, encrypted private messages, and much more!

Shop: Unfolding Nature Unfolding Nature: Being in the Implicate Order   Myyco.com Golden Teacher Liquid Culture For Sale

Jump to first unread post Pages: 1 | 2 | 3 |  [ show all ]
The official ask math questions thread
    #20027680 -

Post any math question here that you're working on, *and I will try to answer*

I'm currently working on:

1. Prove that a continuous function on a compact set is integrable.
2. Let A and B be m by n and m by m matrices. Prove that I_m - AB is invertible if and only if I_n - BA is invertible.

Edited by Satira (05/23/14 02:04 AM)

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Satira]
    #20027685 -

1+1=???

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Waffle]
    #20027713 -

Evaluate ∫(1/(1+x^5))dx.
Note that –1 = –1(cos0°+i sin0°)
∴the roots of the equation x^5+1 = 0 are
(–1)^(1/5) (cos((0°+360k°)/5)+i sin((0°+360k°)/5)) , where k = 0, 1, 2, 3, 4
= –1(cos0°+i sin0°) , –1(cos72°+i sin72°) , –1(cos144°+i sin144°) , –1(cos216°+i sin216°) , –1(cos288°+i sin288°)
= –1 , –cos72°–i sin72° , cos36°–i sin36° , cos36°+i sin36° , –cos72°+i sin72°
∴x^5+1
= (x+1)(x+cos72°+i sin72°)(x–cos 36°+i sin36°)(x–cos 36°–i sin36°)(x+cos 72°–i sin72°)
= (x+1)((x–cos36°)²+sin²36°)((x+cos72°)²+sin²72°)
= (x+1)(x²–2x cos36°+cos²36°+sin²36°)(x²+2x cos72°+cos²72°+sin²72°)
= (x+1)(x²–2x sin54°+1)(x²+2x sin18°+1)
For finding the EXACT value of sin18° and sin54°,
Consider 3×18° = 90°–2×18°
sin(3×18°) = sin(90°–2×18°)
sin(3×18°) = cos(2×18°)
3sin18°–4 sin³18° = 1–2 sin²18°
4sin³18°–2sin²18°–3sin18°+1 = 0
(sin18°–1)(4sin²18°+2sin18


--------------------
we are the universe contemplating its self.

Edited by evileye001 (05/23/14 01:47 AM)

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Waffle]
    #20027721 -

How is the addition function defined on the natural numbers? Can you prove to me that 1 + 1 is 2?

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Satira]
    #20027733 -



--------------------
we are the universe contemplating its self.

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Satira]
    #20027734 -

i'm the one asking questions here.

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Waffle]
    #20027749 -

Got it, I'm asking for clarification. I don't know how you've defined the + function.

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Satira]
    #20027754 -

it's a cross like the one baby j-bird was crucified on.

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Waffle]
    #20027756 -

I predict that this thread will have many questions and few answers.

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Waffle]
    #20027758 -

So you're telling me what the symbol looks like, not how it acts on the elements 1 and 1.

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Satira]
    #20027762 -

all the answers are in the good book.

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Waffle]
    #20027776 -

divide by zero


--------------------
EVERYTHING EVENTUALLY BECOMES A DESERT


Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: 4HO-DMT]
    #20027788 -

I'll post answers to my questions once I've made more progress.

As for progress already on a question, I was working through Lemma 2.1 in Fred Galvin's proof of the Dinitz conjecture, and am still trying to understand the proof fully of Lemma 2.1 in his paper.
Link:  http://www.sciencedirect.com/science/article/pii/S0095895685710118

I am stuck on justifying one step, on how to prove a strict inequality for all v in K, f(v) - 1 > sum over all g(w) for w in N(v)

I have just defined the notation and concepts used specifically in the paper.

Notation:
Consider G to be a digraph
Zn = non negative integers
N(v) = {w in V | (v,w) is in E(G)}
V = V(G)
C = set of "colors". just a countable set.

Concepts:
1. independent set: a set of vertices such that no two vertices have a directed edge in either direction
2. kernel: an independent subset S of V such that for every v in V - S, there exists a w in S such that there is a directed edge from v to w.
3. (f:g)-choosable, where f and g both defined from V to Zn :
graph satisfies this property if,
for an assignment to V based on any function A: V -> Powerset(C) that satisfies, for each v in V, |A(v)| = f(v),
for every v and v' that share an edge,
there exist subsets of A_v and A_v' sized g(v) and g(v') respectively, that are disjoint

Lemma 2.1:
Consider a digraph G such that every subdigraph has a kernel and given functions f and g from V(G) to non negative integers, for all v in V(G) with g(v) > 0, f(v) >= sum over all g(u) where u is in N(v). Then, G is (f:g)-choosable.

Proof summary:
Assume W = {v in V | g(v) < 0} is non empty since case of g(v) = 0 holds since every graph is f:g choosable for a g that maps every vertex to 0.
Consider any color c in the union of A_v for all v in W
S = {v in W | c is in A_v}.
K is any kernel of the subdigraph of G induced by vertex set S. K exists by definition of G.
Define g': V -> Zn, g'(v) = g(v) - 1 for v in K and g(v) otherwise. Since K is contained in S, contained in W, this is a well defined map.
Define f': V -> Zn, f'(v) = f(v) - 1 for v in S and f(v) otherwise.

This is where I am confused, on how the definition of f' satisfies the property, f'(v) >= sum over all g'(u) where u is in N(v), for each v in K.
There are three sets to consider to prove the above property holds:
1. V - S: for all v in V - S, f'(v) = f(v) and for all w in V, g'(w) <= g(w), so definition satisfied.
2. S - K: |N(v)| >= 1 for all v in S - K, by the definition of a kernel. so for all v in S - K, f'(v) = f(v) - 1 >= a*(g(u) - 1) where a is the size of the set of vertices in K which v has a directed edge to (a is at least 1 by kernel def), + sum over all g(w) in N(v) where w in V - K = sum over all g'(u) where u is in N(v). So, definition satisfied.
3. K: This is the case I am confused on how to prove. for all v in K, f'(v) = f(v) - 1, so need to show that f(v) - 1 >= (sum over all g(u) where u is in N(v)) - 1. Perhaps there is an obvious step missing to prove this..

Ok, so then, assuming I know how to prove this case for K, because f' has the desired property for all v in V:
By the inductive hypothesis, G is f':g' choosable and thus, for each v in G there exists a g'(v) sized subset B'_v that satisfies the disjoint condition with B'_w for each w in N(v). Importantly, for every v in S, B'_v does not contain c.
For all v in K, define B_v to be B'_v U {c}, and B'_v otherwise. Thus, |B_v| = |B'_v| + 1 for v in K, and |B_v| = |B'_v| otherwise. This definition agrees with how g maps V.
Since every v in V - K does not contain c, and because K is an independent set, for every v in K, N(v) is contained in S - K. Thus, by the definition of B_v, for every v in K, B_v is disjoint from B_w for every w in N(v). For every v in V - K, B_v = B'_v, so, for every w in N(v), if w is in K, since B'_v is disjoint from B'_w, and B_v does not contain c while B_w does, B_v and B_w remain disjoint. If w is not in K, B_w = B'_w, so B_v and B_w remain disjoint. Thus G is (f:g)-choosable. ||

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: 4HO-DMT]
    #20027797 -

I thought the Shroomery would be full of math enthusiasts given the highly complex nature of the psychedelic experience :shrug:

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: evileye001]
    #20027810 -

Are you stuck on evaluating the integral ?

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Satira]
    #20027907 -

It's almost the end of may. The fuck you doing math for?


--------------------

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Dark_Star]
    #20027924 -

I'm self studying math!

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Satira]
    #20027935 -

:postscore: = ?


--------------------
*
Live by the mushroom, die by the mushroom
:mushroom2::rainbowdrink:
This is a trap! A trap! You are all busted! Busted! You fools!
:twirlyface:

If a time comes where I fail to appear I've been abducted and I will miss you all
Please smile and pet puppies as often as possible
Be happy
Be nice
(<3);}

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Satira]
    #20027936 -

:archiebunker:


--------------------

Extras: Filter Print Post Top
Re: The official ask math questions thread [Re: Dark_Star]
    #20027943 -

I have a job, this is more to keep my mind sharp and my bullshit detector well oiled.

Extras: Filter Print Post Top
Jump to top Pages: 1 | 2 | 3 |  [ show all ]

Shop: Unfolding Nature Unfolding Nature: Being in the Implicate Order   Myyco.com Golden Teacher Liquid Culture For Sale

Community > The Pub
Threaded Mode Threaded  Previous topic Previous  View all topics Index  Next topic Next 

Similar ThreadsPosterViewsRepliesLast post
* RAAAAAAAWH (Official Punk Song Thread)
( 1 2 all )		 Cracka_X 6,793 39 10/24/24 08:17 PM
by 073202
* Official Search Assistance Thread!
( 1 2 3 all )		 PapaverS 9,397 54 12/06/02 02:29 AM
by Papaver
* *Official Amanda photo thread* NO FLAMES
( 1 2 all )		 LearyfanS 12,546 31 12/11/02 05:13 PM
by Papaver
* Mexicali Blues (official cowboy song thread)
( 1 2 3 all )		 Ripple 11,020 52 07/09/11 03:17 AM
by ModularMind
* Free Association Thread
( 1 2 3 4 ... 28 29 )		 RebelSteve33 35,553 563 12/10/05 07:22 AM
by detergent
* Official Dead tour post
( 1 2 3 4 all )		 Ripple 10,938 60 07/02/03 02:31 PM
by Ripple
* Sheekle Respect Thread
( 1 2 3 4 ... 14 15 )		 Canadian Jesus 13,059 294 03/17/18 04:18 PM
by watermelon mon
* *Official*...what r u going to be for holloween?
( 1 2 3 all )		 40oz 6,202 56 10/30/02 01:04 AM
by Baby_Hitler

Extra information
You cannot start new topics / You cannot reply to topics
HTML is disabled / BBCode is enabled
Moderator: Entire Staff
3,625 topic views. 1 members, 38 guests and 370 web crawlers are browsing this forum.
[ Show Images Only | Sort by Score | Print Topic ]
Search this thread:

Copyright 1997-2026 Mind Media. Some rights reserved.

Generated in 0.032 seconds spending 0.008 seconds on 18 queries.