Then what is this cognizer entity, cognising? @user284982 $\emptyset \neq \{\emptyset\}$. Read Lakatos and you'll be ahead of most college students (and maybe even many professors of mathematics) in understanding how math really works -- what all those definitions and axioms and proofs do for you. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. ∅ E.g. Maybe someone knows if the null is transmitted this way: Or is "null" just the "high-but-inactive line" represented here by ...111111111111111111... ? If one can show that the notion of nothing is indeed required in the argument which claims "nothin can exist", then "nothing exists" must be entertained as a TRUE statement. “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…. (\phi<<\math>) are not the symbol for the empty set in mathematics, and should not be used as such in Wikipedia. - leave it undefined? This would truly be "null", i.e. If anyone knows the title of this book, and, even better, how I might go about obtaining a copy (I didn't see him in a search on Amazon, for example), I would greatly appreciate this. So, what is platonic paradigm being formed which itself uses reality, which may not itself subscribe completely to platonic notions. So, if the universal set doesn't exist in a set theory, what does that theory do about the complement of the empty set? I have made the article use the symbol ∅ consistently. We all know about Ø, and that it was created by the Bournaki group, but I've never seen a good explanation of why it was chosen. Read it the first time without the footnotes -- it's a pretty easy read until the last chapter. If you think it is illogical to talk of an empty set, how about the number zero? A set $A$ is a subset of another set $B$, written $A\subseteq B$, if and only if for every $a\in A$ you must also have $a\in B$. The sets {a}, {1}, {b} and {123} each have one element, and so they are equivalent to one another. The empty set is a set. ϕ It is directly contradicted by the axiom of regularity, and its existence would cause paradoxes which would make the theory inconsistent. What exactly limits the signal frequency on transmission lines? On the other hand, it is true that it would be valuable to explain the background and motivation of concepts, both historically and philosophically, but that is hard. @ user, what does it mean to be a subset of? Lesson: all atomic axioms of a Logic system must acknowledge consciousness as a required cognising / advertising entity, which itself cannot be made "zero", for if it made zero then nothing can even be uttered, leave alone "established". I don't think it's quite correct the way it stands. S} for any nonempty set S? Why do people call an n-sided die a "d-n"? I've tried to compensate for deleting this by giving the briefest mention of how intuition can conflict with the formal definition of a set. I don't see why you don't want to have an example of what we're talking about. However Cantor did not adopt Menge and Mengenlehre as the terms until later. As he pointed out, {{}} is the set containing the empty set. I have never seen anyone else use this notation, in many years as a mathematician. Another example: In 7-bit + parity ASCII teletype code the NULL is 0008, i.e. Asking for help, clarification, or responding to other answers. First, how can you say that "What is the complement of A?" They are not the same thing. What is the minimum viable ecological pyramid a terrafoming project would introduce to world with no life to make it suitable for humans? You can formalise it as an ordered pair (A,X), where A is a subset of X (just as you can formalise a function as an ordered pair (G,Y), where G is the graph and Y is the codomain). But if your colleague treats {} specially in this regard, then I'm afraid that I can't help him.