# Thursday April 13th

## 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 (one-to-one) : map by at most one element

• Surjective (onto) : map by at least one

• Bijective (one-to-one 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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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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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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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 :(
Written on April 13, 2017