Chapter 20, Shorthand Symbols
as Pronouns
1. Pronouns and Shorthand
Symbols
The words it, you, I, he and she are
pronouns. They can be used to refer to objects or individuals. Further,
from time to time, these pronouns are used to refer to different objects
and different people. The meaning of each pronoun can last for just a
short while, before the given meaning is forgotten or changed. Pronouns
and nicknames provide short ways for talking and writing about objects
and people. Pronouns provide a form of shorthand useful in both algebra
and (symbolic or mathematical) logic. Letters may serve as pronouns in
algebra and logic. Got it?
2. Pronouns and Shorthand
Labels
There is only one pronoun it. For each object we meet or
have met, we could say it. But if I say
it, which object do I mean? The word it
is easily overused. The single pronoun it is not enough
for us. We need more.
To overcome this difficulty of not having enough pronouns, we may invent
our own names, labels or pronouns for people and objects. Then in
speaking about a person or object, we use a name, label or individual
pronoun. Here letters and other symbols (the choice is wide) can serve as
short names, labels or extra pronouns. We can have one name or pronoun
for each person or object we talk about.
In logic, we can talk about events like (i) Aunt Jane visits, (ii) the
cat climbs a tree, or (iii) Tom plays. In speaking about one of these
events we could use the pronoun it, or we could mention
the name of the event, or we could provide a temporary (?) shorthand
label. For example, we can talk about event A, or event B. The shorthand
letters here serve as names or extra pronouns. So we can say event A, or
event B, or event M. For more labels, we can number the people or
objects. This further helps to identify them. For instance, we can refer
to the first situation A, the second situation B, the third situation C
.... Doing both, that is assigning numbers and labels is acceptable,
although this introduces redundancy.
3. Shorthand Notation
One way implication rules can be written in many forms. For instance, the
four phrases in the left column of the following table all have the same
meaning. To avoid writing these phrases in their longhand form, we can
use compact, or more compact shorthand notation (symbols), etc.
|
Phrase
|
Shorthand Notation
|
|
if A then B
|
A => B
|
|
A implies B
|
A => B
|
|
B if A
|
B <= A
|
|
B is implied by A
|
B <= A
|
Compact forms for the shorthand phrase A if and only if
B are given by A iff B and by AÛ
B. In place of A if and only if B, we may say
situation A is equivalent to situation B or, more briefly, A is
equivalent to B. The four phrases in the left column of the next
table all have the same meaning and the same shorthand form.
|
Phrase
|
Shorthand Notation
|
|
A is equivalent to B
|
A <=> B
|
|
A if and only if B
|
A <=> B
|
|
A iff B
|
A <=> B
|
|
A when and only when B
|
A <=>B
|
The four phrases and the shorthand notation A Û B are
interchangeable. We can use one in place of any other as we like or just
for the sake of variety while talking or writing.
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
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Road
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See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for
justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning
first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon
due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions
by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate
is not compensation for years or decade
of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern
Based Reason may slowly lead to greater precision in reading, applying and
writing laws.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
allow parents unsure of themselves in mathematics to help their
children. The selection acquired in Canada is published in the
USA. So it has a US orientation. In retrospect, the selection
shows parents what to check with the booklets or by other ways,
the choice is theirs. But in retrospect, the selection does not
cover integral and fractions liquid weights and measures - ask
the publishers to correct that! For ages 9 to 12 say, parents may
compensate by showing boys and girls how to use weights or mass,
and further measures in food preparation. Beyond that children
may be shown how to measure and calculate angles, lengths and
areas [proportional amounts too] directly or by using maps and
plans drawns to scale. Learning how to gather and measure all the
ingredients, pots and pans for a dish or a meal, along with
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McCainian: drill, drill, drill then Toronto
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Mathematics
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Skills with take
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Basic skills include
time-date-calendar Matters; money matters; map, plan and
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Is your child able to add, subtract and multiply amounts
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work with maps and plans, and measure length, weight-mass and
volume? Schools may promote your son or daughter without
providing basic skills in reading, writing and
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Arithmetic
and Number Theory Skills
Algebra
Starter Lessons
Geometry
- maps plans trigonometry vectors
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Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
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How to Ace Calculus: Street Wise Guide - Mostly
Text.
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Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
trespassed in the house of the three bears, she found three bowls
of porridge, two not to her liking, and one just right. Different
bears have different tastes. As invited guest here and elsewhere,
if one or more explanations is not to liking, try another. It may
be better or just right.
Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
way may go deeper and farther than those with none. High marks,
if the come easy, may be deceptive - provide a too light and not
a deep mastery. That could have been your problem in secondary
school, one that leads to comprehension shock or difficulties in
calculus and more generally in the first year of college. Bon
Appetite.
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