According to a Wikipedia article on the subject, in Herbert B. Enderton's book Computability: An Introduction to Recursion Theory (2011), even if nowhere else (no other reference is given, and I've never seen the usage):
Answer from Calum Gilhooley on Stack ExchangeIf
is a partial function on
and
is an element of
, then this is written as
and is read as "
is defined."
If
is not in the domain of
, then this is written as
and is read as "
is undefined".
According to a Wikipedia article on the subject, in Herbert B. Enderton's book Computability: An Introduction to Recursion Theory (2011), even if nowhere else (no other reference is given, and I've never seen the usage):
If
If
I have never seen such a symbol. I don't think it would be very useful, and it might make unexperienced people less aware that they are dealing with an undefined entity, and start doing calculations with it getting meaningless results.
According to a Wikipedia article on the subject, in Herbert B. Enderton's book Computability: An Introduction to Recursion Theory (2011), even if nowhere else (no other reference is given, and I've never seen the usage):
Answer from Calum Gilhooley on Stack ExchangeIf
If
Okay, so this question came out of a question I had about how np.NaN behaves in the numpy python library. Apparently np.NaN is defined to behave like "undefined" in math, which leads to the counterintuitive - to me at least - result that np.NaN does not equal itself.
So
undefined != undefined...
We also know things like
x/0=undefined (or maybe we can't use equality here? x/0 *is* undefined?)
That means that we know some things about it...whatever it is. What branch of math do we use to learn things about "undefined"?
What kind of formal system does "undefined" belong to? Is it a theorem in ZFC set theory? Like is it some kind of set? Its not the "null" set right?
I hope I have made my profound ignorance on this subject clear enough, maybe someone here can meet me 99% of the way and help drag me toward the light.
Hey everyone, I want to share a new idea I had about the infamous 0 divided by 0 problem in math.
We all know that 0 ÷ 0 is considered undefined because any number multiplied by zero equals zero — so there’s no single answer. But what if instead of saying "undefined," we define a new symbol to represent all possible answers?
I propose using Ⓐ, the circled A, where:
The circle means “no fixed start or boundary,” representing infinite possibilities
The A stands for “All numbers” that satisfy the equation
So,
0 \ 0 = Ⓐ
and by definition,
Ⓐ * 0 = 0
This symbol gives us a clean way to express the indeterminate form 0 ÷ 0 as a set of all solutions rather than leaving it undefined.
It’s kind of like how π represents a special constant for circles — Ⓐ could be the symbol for this “all solutions” concept.
What do you think? Is this a useful way to think about or represent the problem? I’d love to hear your thoughts!
pls give credit when this symbol come used in math