Thursday April 13th
4/13/17  Zariski and Table Troubles
Today I learned:
 Starting to get a bit of intuition for Grothendieck (usually denoted by Tau). I particularly like this quote by Taylor Dupuy’s Math Vlog:
“if you have a covering and you cover the covering, (that) the covers of the covering give you a covering” :)
 However, Zariski sites are a bit of a mystery. I’m learning
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Injective (onetoone) : map by at most one element

Surjective (onto) : map by at least one

Bijective (onetoone and onto) : map by exactly one
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Homework 1.2.3.1
Let x and y be variables that take on integer values. Let p be the statement that x is positive and q be the statement that y is positive. Determine the symbolic statements for the following predicates described using English. Mark all that are appropriate.
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Answers:
Both x and y are positive.
 p AND q
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Either x or y is positive.
 p OR q
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x is positive but y is not.
 p OR (not q)
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Either x or y but not both are positive.

(p OR q) AND (not(p AND q))

(p AND (not q)) OR ((not p) AND q)
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x is not positive and y is not positive.
 (not p) AND (not q)
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At least one of x and y is not positive.

(not(p AND q))

(not p) OR (not q)
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Neither x nor y is positive.
 (not p) AND (not q)
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It is not the case that both x and y are positive.
 (not(p AND q))
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Both x and y are not positive.
 Not clear
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If x is positive then y is positive.
 p => q
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Homework 1.2.4.1
Let p = F, q = F, and r = F.
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Answers:
p AND q => r
 True
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(p AND q) => r
 True
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p AND (q => r)
 False
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Evaluate T OR (not T) OR F => T OR (not T) <=> T => F.
 True
Basically :

T OR F AND F => T OR F <=> T => F

T OR F AND F => T AND F <=> T => F

T OR T => F <=> F

T => T

= T
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Homework 1.2.5.1
Complete the following truth table: (Enter T or F in each field)
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Answers:
E1  E2  E1 AND E2  E2 AND E1  E2 AND E1 <=> E2 AND E1  

T  T  T  T  T  
T  F  F  F  T  
F  T  F  F  T  
F  F  F  F  T 
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p  q  p AND q  p AND q => q  

T  T  T  T  
T  F  F  T  
F  T  F  T  
F  F  F  T 
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Things to get done:

See if prof opens up quiz so I can take it. C++, that is.

Continue with Matlab, programming for correctness. I’m already starting to see that it is positively affecting my ability to fluently read mathematical notation, which is fantastic.

Continue with Lab for C++ (ie Lab #3, due on the 18th)
Other notes:

Today I meet up with my Mathematician/ numerical computation friend. He usually helps with my understanding, so it’s good to come to him with questions.

This is an interesting book to look at > Zariski Geometries: Geometry from the Logician’s Point of View (Boris Zilber).

Also, Saturated Model Theory > by Gerald E. Sacks, which talks about “Saturated Bubbles” in Model Theory/ MT in general
Bugs
 Formatting errors abound in this template. Numbers not printing, indentation and spacing is off. Had a similar issue with yesterday’s post.
 My markdown table renders beautifully in Github md format, but doesn’t in the actual blog. Right now, LaTeX > Markdown :(