User blog:Edwin Shade/Set Theory

So I know that other than Emlightened herself, most likely no one else fully understands Sasquatch, so I'm going to change that by also learning just what it is with the help of anyone who can comment on this blog post.

This blog post will also attempt to explain in a systematic manner what the meaning of this is, where the definition of Sasquatch has been formally laid out. My belief is that by breaking a chunk of data into smaller parts, and explaining those parts in an easily-digestible way, learning is easier and the difficult becomes easy.

So, to begin with, here is the first sentence:

"We work in the language  ( ∈ , ∈ <span class="mo" id="MathJax-Span-10" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">¯      <span class="mo" id="MathJax-Span-11" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">, <span class="mo" id="MathJax-Span-12" style="transition:none;display:inline;position:static;padding-left:0.18em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">< <span class="mo" id="MathJax-Span-13" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">)      <span style="color:rgb(0,0,0);font-family:Tinos;font-size:medium;font-weight:normal;">, where equality is a defined symbol. <span class="MathJax" data-mathml="" id="MathJax-Element-2-Frame" role="presentation" style="display:inline;font-weight:normal;line-height:normal;font-size:medium;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;color:rgb(0,0,0);font-family:Tinos;position:relative;" tabindex="0"><span class="math" id="MathJax-Span-14" style="transition:none;display:inline-block;position:static;vertical-align:0px;line-height:normal;width:0.71em;"><span style="transition:none;display:inline-block;position:relative;vertical-align:0px;line-height:normal;width:0.652em;height:0px;font-size:16.96px;"><span style="transition:none;position:absolute;vertical-align:0px;line-height:normal;clip:rect(1.477em1000.59em2.42em-999.997em);top:-2.179em;left:0em;"><span class="mrow" id="MathJax-Span-15" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;"><span class="mo" id="MathJax-Span-16" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">∈     <span style="color:rgb(0,0,0);font-family:Tinos;font-size:medium;font-weight:normal;">,  <span class="MathJax" data-mathml="" id="MathJax-Element-3-Frame" role="presentation" style="display:inline;font-weight:normal;line-height:normal;font-size:medium;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;color:rgb(0,0,0);font-family:Tinos;position:relative;" tabindex="0"><span class="math" id="MathJax-Span-17" style="transition:none;display:inline-block;position:static;vertical-align:0px;line-height:normal;width:0.71em;"><span style="transition:none;display:inline-block;position:relative;vertical-align:0px;line-height:normal;width:0.652em;height:0px;font-size:16.96px;"><span style="transition:none;position:absolute;vertical-align:0px;line-height:normal;clip:rect(1.3em1000.59em2.42em-999.997em);top:-2.179em;left:0em;"><span class="mrow" id="MathJax-Span-18" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;"><span class="texatom" id="MathJax-Span-19" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;"><span class="mrow" id="MathJax-Span-20" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;"><span class="munderover" id="MathJax-Span-21" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;"><span style="transition:none;display:inline-block;position:relative;vertical-align:0px;line-height:normal;width:0.652em;height:0px;"><span style="transition:none;position:absolute;vertical-align:0px;line-height:normal;clip:rect(3.305em1000.59em4.248em-999.997em);top:-4.006em;left:0em;"><span class="mo" id="MathJax-Span-22" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">∈  <span style="transition:none;position:absolute;vertical-align:0px;line-height:normal;clip:rect(3.246em1000.42em3.659em-999.997em);top:-4.124em;left:0.062em;"><span class="mo" id="MathJax-Span-23" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">¯           <span style="color:rgb(0,0,0);font-family:Tinos;font-size:medium;font-weight:normal;"> and  <span class="MathJax" data-mathml="" id="MathJax-Element-4-Frame" role="presentation" style="display:inline;font-weight:normal;line-height:normal;font-size:medium;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;color:rgb(0,0,0);font-family:Tinos;position:relative;" tabindex="0"><span class="math" id="MathJax-Span-24" style="transition:none;display:inline-block;position:static;vertical-align:0px;line-height:normal;width:0.828em;"><span style="transition:none;display:inline-block;position:relative;vertical-align:0px;line-height:normal;width:0.769em;height:0px;font-size:16.96px;"><span style="transition:none;position:absolute;vertical-align:0px;line-height:normal;clip:rect(1.477em1000.71em2.42em-999.997em);top:-2.179em;left:0em;"><span class="mrow" id="MathJax-Span-25" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;"><span class="mo" id="MathJax-Span-26" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;font-family:MathJax_Main;"><      <span style="color:rgb(0,0,0);font-family:Tinos;font-size:medium;font-weight:normal;">   are binary predicates, we also define the unary functions  <span class="MathJax" data-mathml="<mi>F</mi>" id="MathJax-Element-5-Frame" role="presentation" style="display:inline;font-weight:normal;line-height:normal;font-size:medium;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;color:rgb(0,0,0);font-family:Tinos;position:relative;" tabindex="0"><span class="math" id="MathJax-Span-27" style="transition:none;display:inline-block;position:static;vertical-align:0px;line-height:normal;width:0.828em;"><span style="transition:none;display:inline-block;position:relative;vertical-align:0px;line-height:normal;width:0.769em;height:0px;font-size:16.96px;"><span style="transition:none;position:absolute;vertical-align:0px;line-height:normal;clip:rect(1.3em1000.77em2.361em-999.997em);top:-2.179em;left:0em;"><span class="mrow" id="MathJax-Span-28" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;"><span class="mi" id="MathJax-Span-29" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">F      <span style="color:rgb(0,0,0);font-family:Tinos;font-size:medium;font-weight:normal;"> and  <span class="MathJax" data-mathml="<mi>R</mi>" id="MathJax-Element-6-Frame" role="presentation" style="display:inline;font-weight:normal;line-height:normal;font-size:medium;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;color:rgb(0,0,0);font-family:Tinos;position:relative;" tabindex="0"><span class="math" id="MathJax-Span-30" style="transition:none;display:inline-block;position:static;vertical-align:0px;line-height:normal;width:0.828em;"><span style="transition:none;display:inline-block;position:relative;vertical-align:0px;line-height:normal;width:0.769em;height:0px;font-size:16.96px;"><span style="transition:none;position:absolute;vertical-align:0px;line-height:normal;clip:rect(1.3em1000.77em2.361em-999.997em);top:-2.179em;left:0em;"><span class="mrow" id="MathJax-Span-31" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;"><span class="mi" id="MathJax-Span-32" style="transition:none;display:inline;position:static;vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">R      <span style="color:rgb(0,0,0);font-family:Tinos;font-size:medium;font-weight:normal;"> from these."

In the comments below, can someone please explain what this means in layman's terms, and then in depth terms ?

<span class="MathJax" data-mathml="<mi>F</mi>" id="MathJax-Element-5-Frame" role="presentation" style="display:inline;font-weight:normal;line-height:normal;font-size:medium;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;color:rgb(0,0,0);font-family:Tinos;position:relative;" tabindex="0"><span class="math" id="MathJax-Span-27" style="transition:none;display:inline-block;position:static;vertical-align:0px;line-height:normal;width:0.828em;"><span style="transition:none;display:inline-block;position:relative;vertical-align:0px;line-height:normal;width:0.769em;height:0px;font-size:16.96px;"><span style="transition:none;position:absolute;vertical-align:0px;line-height:normal;clip:rect(1.3em1000.77em2.361em-999.997em);top:-2.179em;left:0em;">