Avengers
9.0
Monday, 4 December 2017
Sunday, 3 December 2017
Math 101 - Lecture 9 Revision
Maths
101 – Lecture 9 Revision
Supermum x 
k
for x 
S
k
for x S
And
K -
x
for some x S
and > 0
x
for some x S
and > 0
Infinum k 
x,
for all x S
and k +> x, for some x S
and any > 0.
x,
for all x S
and k +> x, for some x S
and any > 0.
Eg 1
s1 = { x Q x ½
}
Q x ½
}
2 s2 = { x Q x2
< 2 }
Q x2
< 2 }
3
s3 = { ½, 2/3, ¾, ... n/(n + 1), ... }
4
s4 = { 1, ½, ¼, ... 2-n }
Which sets are bounded? What are the
supermum and infinmum?
Solutions
1 Bounded Supremum is ½ and is contained in S.
Infinmum is 0 and is contained in S.
2 Boundednote S2
= { x Q :
- √2 < x √2}
Q :
- √2 < x √2}
Supremum
is √2, note √2 is not in S2
Infinmum
is -√2, note √2 is not in S2
3 Bounded Supremum
is 1, note 1 is not in S3
Infinmum
is ½, note ½ is in S3
4 Bounded Supremum
is 1, note 1 is in S4
Infinmum
is 0, note 0 is not in
-//-
Complex numbers
Any equation x2 = a, a R
R
Cannot be solved for x R,
if a < 0
R,
if a < 0
Extend R so that x2 = -1 has a
solution
Yes can solve it in C (Complex numbers)
C is R with an element I = √-1 (and its
multiples etc)
Note R ⸦ C
Any complex number z C,
can be put into the form z = a +ib; a, b R
C,
can be put into the form z = a +ib; a, b R
a = Real part of z = a + ib, Re(z) = a
b = Imaginary part of z, a + ib, Im(z) = b
eg 2 – 3i C
C
Re(2-3i) = 2
Im(2-3i) = -3
Addition of elements C
Eg (2-3i) + (1+i) = 3 – 2i
Note: Re(z1 + z2) =
x1 + x2
Im (z1 + z2) = y1
+ y2
Multiplication
Eg (2 – 3i)(1 + i) = 2 + 2i – 3i – 3i2
=
2 – i – 3i2, but i2 =
-1
=
2 – i – 3 – 1
=
5 – i
General z1
= x1 + iy1
Z2
= x2 + iy2
z1z2 = (x1
+ iy1)( x2 + iy2) = x1x2 + ix1y2 + iy1x2
+ i2y1y2
= x1x2 – y1y2
+ i(x1y2 + x2y1)
(a)
(2
+ 3i)(10 – i) = 20 – 2i + 30i – 3i2
= 23
+ 28i
(b)
(1
+ i)2 = (1 + i)(1 =
i) (c) (√2 - i)2 = (√2)2 + (-i)2 -
2√2i
= 1 + i + i + i2 = 2 – 1 -
2√2i
= 2i =
1 - 2√2i
(d) i3 = i2i = -i
(e) i4 = (i2) = (-1)2
= i
(f) i5 = i ,
Molluscs
https://www.nature.com/articles/ngeo1635: Extensive dissolution of live pteropods in the Southern Ocean | Nature Geoscience
https://news.nationalgeographic.com/news/2011/04/110414-eyes-rock-crystal-mineral-chiton-mollusk-vision-animals-science/: Eyes Made of Rock Really Can See, Study Says
https://www.nationalgeographic.com/animals/invertebrates/g/giant-squid/: Giant Squid | National Geographic
https://en.wikipedia.org/wiki/Glaucus_atlanticus: Glaucus atlanticus - Wikipedia
https://en.wikipedia.org/wiki/Janthina_janthina: Janthina janthina - Wikipedia, the free encyclopedia
http://www.scientificamerican.com/podcast/episode/octopus-skin-senses-light-no-eyes-or-brain-needed/: Octopus Skin Senses Light, No Eyes or Brain Needed - Scientific American
https://news.nationalgeographic.com/news/2011/04/110414-eyes-rock-crystal-mineral-chiton-mollusk-vision-animals-science/: Eyes Made of Rock Really Can See, Study Says
https://www.nationalgeographic.com/animals/invertebrates/g/giant-squid/: Giant Squid | National Geographic
https://en.wikipedia.org/wiki/Glaucus_atlanticus: Glaucus atlanticus - Wikipedia
https://en.wikipedia.org/wiki/Janthina_janthina: Janthina janthina - Wikipedia, the free encyclopedia
http://www.scientificamerican.com/podcast/episode/octopus-skin-senses-light-no-eyes-or-brain-needed/: Octopus Skin Senses Light, No Eyes or Brain Needed - Scientific American
Saturday, 2 December 2017
Church notes - 3rd December 2017
1 Chronicles 16:23 -27
Psalm 42
Big Questions - The Psalmist is distressed
vs 2, 3
What is going on?
Not questions of disrespect
Questions of genuine confusion
Deep down God hasn't forgotten him, it just feels like it.
- Look at the world today!
- Despair from grief
- Relationship breakdown
The world tries to get answers
- Despair
- - distract yourself!
- - give up!
Very short sighted answers
God does care
He is interested in all the big and small things in your life.
Three actions
Remember
The presence and faithfulness of God.
vs 4
God was present in the past. He is present in the here and now.
vs 6 - 8
Painting a picture of his life.
- Feeling like he's drowning?
Feelings - like their's no hope.
Knowledge of the truth
- Remembering God's Character and Actions
Preach
Preaching to yourself God's truth
Battle between the mind and spirit.
Don't let the Devil infiltrate your feelings
We need to be waiting patiently upon God's timing.
Isaiah 40:31
Not a peaceful Psalm, a desperate situation
We need to see our need for Him as a necessity.
- An Instinct
Jonathan Edwards - "The Enjoyment of God is the only happyness with which our souls are satisfied."
vs 11
Psalm 42
Big Questions - The Psalmist is distressed
vs 2, 3
What is going on?
Not questions of disrespect
Questions of genuine confusion
Deep down God hasn't forgotten him, it just feels like it.
- Look at the world today!
- Despair from grief
- Relationship breakdown
The world tries to get answers
- Despair
- - distract yourself!
- - give up!
Very short sighted answers
God does care
He is interested in all the big and small things in your life.
Three actions
Remember
The presence and faithfulness of God.
vs 4
God was present in the past. He is present in the here and now.
vs 6 - 8
Painting a picture of his life.
- Feeling like he's drowning?
Feelings - like their's no hope.
Knowledge of the truth
- Remembering God's Character and Actions
Preach
Preaching to yourself God's truth
Battle between the mind and spirit.
Don't let the Devil infiltrate your feelings
We need to be waiting patiently upon God's timing.
Isaiah 40:31
Not a peaceful Psalm, a desperate situation
We need to see our need for Him as a necessity.
- An Instinct
Jonathan Edwards - "The Enjoyment of God is the only happyness with which our souls are satisfied."
vs 11
Friday, 1 December 2017
November 2017 Writings Overall List
November Writings
2017
4th
:
,http://fardell34.blogspot.com/2017/11/4th-november-2017-writings.html
https://twitter.com/fardell24/status/926764665123700737
6th
:
http://fardell34.blogspot.com/2017/11/6th-november-2017-writings.html,
https://twitter.com/fardell24/status/927499156993617920
7th
:
http://fardell34.blogspot.com/2017/11/7th-november-2017-writings.html,
https://plus.google.com/u/0/+ChristopherFardell/posts/fmGQsXCcyic
8th
:
http://fardell34.blogspot.com/2017/11/8th-november-2017-writings.html,
https://twitter.com/fardell24/status/928224084789358592
10th
:
http://fardell34.blogspot.com/2017/11/10th-november-2017-writings.html,
https://twitter.com/fardell24/status/928958372761681921
14th,
15th :
http://fardell34.blogspot.com/2017/11/14th-15th-november-2017-writings.html,
https://plus.google.com/u/0/+ChristopherFardell/posts/WZGujCHrj47
16th,
17th
:
http://fardell34.blogspot.com/2017/11/16th-17th-november-2017-writings.html,
https://twitter.com/fardell24/status/931497209660448769
19th
:
http://fardell34.blogspot.com/2017/11/19th-november-2017-writings.html,
https://plus.google.com/u/0/+ChristopherFardell/posts/NSj1VbjwG5f
21st
:
http://fardell34.blogspot.com/2017/11/21st-november-2017-writings.html,
https://twitter.com/fardell24/status/932936625364930560
22nd
:
http://fardell34.blogspot.com/2017/11/22nd-november-2017-writings.html,
https://plus.google.com/u/0/+ChristopherFardell/posts/Tci3JRydm28
23rd,
24th
:
http://fardell34.blogspot.com/2017/11/23rd-24th-november-writings.html,
https://twitter.com/fardell24/status/934188955037188096
25th
:
http://fardell34.blogspot.com/2017/11/25th-november-2017-writings.html,
https://plus.google.com/u/0/115245633245722817719/posts/VDSjHrSax4D
26th
:
http://fardell34.blogspot.com/2017/11/26th-november-2017-writings.html,
https://plus.google.com/u/0/+ChristopherFardell/posts/Sf1jXjvm2r1
27th
- 29th
:
http://fardell34.blogspot.com/2017/12/27th-29th-november-writings.html,
https://twitter.com/fardell24/status/936507653261467648
Overall Total: 7783
27th - 29th November Writings
27th - 29th
Excerpt from: Adventures in Armidale – Armidale at night
Daniel and Tia emerged from one of the Block 1 upstairs balconies
onto the roof of the Kitchen.
Words: 18
Excerpt from: After the Plague in New England v2
27 May 2020
The Constitutional Referendum is held. The current constitution is
voted for by 60%.
Words: 16
Excerpt from: Ages of Change – Future Timeline
Wednesday,
20 December 2017
Star
Wars: The Last Jedi
breaks the record for the most money made in the first week of
release.
Thursday,
21 December 2017
Another
record broken by The
Last Jedi,
the most rewatchers.
Friday,
22 December 2017
Disney
announces the next Star
Wars Anthology
film will be released next December.
Saturday,
23 December 2017
The
Last Jedi
cinema attendance declines.
24
– 29 December 2017
Protests continue in Australia regarding the lack of legalisation of
Same Sex Marriage.
Sunday,
24 December 2017
Many Churches in Sydney find themselves the target of pro-Same Sex
Marriage protests.
Monday,
25 December 2017
Twice
Upon a Time,
the latest Christmas Special for Doctor
Who
airs. Jodie Whitaker makes a great impression during her inaugural
scenes as the Thirteenth Doctor.
Tuesday,
26 December 2017
Various
Doctor Who
fan sites go down from the web traffic related to the previous day's
episode.
30
December 2017 – 6 January 2018
Many terrorist attacks are thwarted through the New Year Period.
January 2018
After some delay and protests, Same Sex Marriage is legalised in
Australia.
7
January – 13 January 2018
Many LGBTIA activists protest in Canberra...
14 – 20 January
2018
Protests
continue in Canberra, while Parliament resumes after the Christmas –
New Year break.
Sunday, 14 January
2018
Across
the country, various Church congregations pray about the week ahead.
Monday, 15 January
2018
Parliament
resumes after the Christmas – New Year break.
Tuesday, 16 January
2018
The
House of Representatives revisits the Same Sex Marriage legislation,
again.
Wednesday, 17
January 2018
The
House of Representatives amends the Same Sex Marriage legislation,
including further religious protections.
21 – 27 January
2018
The
Federal Parliament finally passes the Same Sex Marriage legislation,
with religious protections included.
28 January – 3
February 2018
Two more MPs resign due to being dual citizens.
4
– 10 February 2018
With Same Sex Marriage legalised, Shorten turns his attention to
bringing about a Royal Commission into the Banking System.
The Winter Olympics at PyeongChang in South Korea start.
11 – 17 February
2018
The Winter Olympics continue, with many records being broken.
18 – 24 February
2018
As the Winter Olympics come to an end, North Korea increases military
activities on their side of the DMZ. Kim Jung-Un continues to goad
POTUS Donald Trump...
25
February – 3 March 2018
More build-up to a possible war on the Korean Peninsula occurs. The
American Establishment fails at trying to rein in Trump, as much as
it has done for the past year.
Words: 423
Excerpt from (Silent) Reverse Map Game: 2017 Edition
1895
Americas
The
proportion of Minnesota Norse speakers in Midgard County drops below
69%.
In
eastern Minnesota overall, the number drops below 31%.
In
Minnesota overall, the number drops below 16%.
Within
the US overall (excluding Minnesota) it drops below 2%.
Europe
As
England continues to centralise, the Northumberland Assembly is
abolished.
The
German rebellion continues to grow more serious.
Africa
...
Asia
Australasia
Antipodea
New
South Wales
Armidale's
population reaches 2800.
Dubbo's
population reaches 4250.
Words: 76
Total: 533
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