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I'm searching for two symbols - considering they exist - (1) unknown value; (2) unknown probability.

Note: I thought that $x$ was used in a temporary context, whenever I see it, it remains unknown until an evaluation is made. I was thinking in a "unknown and impossible to be known" context. I'm not sure if this context exists or if $x$ also express it.

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$x{}{}{}{}{}{}{}$ –  t.b. Sep 12 '12 at 12:26
    
You can choose any symbol you like actually. –  ᴊ ᴀ s ᴏ ɴ Sep 12 '12 at 12:58
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With regard to the edit: It is impossible to know whether $x=1$ or $x=-1$ in $x^2=1$. –  Michael Greinecker Sep 12 '12 at 13:01
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We must know what we are talking about. That is by definition we must be able to express it. Else, we do not talk about the quantities we don't know. However, some things can be expressed in a limited way, and yet cannot be evaluated. For example, we do not talk about infinite sums, we only talk about limits of infinite sums. So, what is the sum of an infinte series? We say we can not evaluate it, however, if you take so and so many finite terms, the series will be withing this range of the "limit". In that case, then we can use $x = \lim_{n \rightarrow \infty} \sum a_{n}$ –  Jayesh Badwaik Sep 12 '12 at 14:17
    
@MichaelGreinecker It's impossible, but since $x^2=1$ for $x=1$ and $x=-1$, can't we assume that we have a set of two numbers that answers the question $x^2=?$ and thus accepting it as possible to be known? –  Vladimir Putin Sep 13 '12 at 0:49

6 Answers 6

up vote 3 down vote accepted

As the others already mentioned. There are conventional variables to the unknowns such as $x$ for an unknown value or $P(A)$ for an unknown probability. We take them as variables and assume that they are unknown however there is a certain probability that they take some reasonable values. That is actually the reason why we define them.

Additionally in computer programming there is a term called 'NaN:=Not a Number'. That is also somehow an unknown value, However even worse, we dont have any hope that it can be as in the case $x$. They are often mentioned as Indeterminate_forms arising from $0/0$, $\infty-\infty,\infty/\infty$ etc..

There might be also another interpretation to understand an unknown probability. If you have a probabilistic model and If you have deviations from the model assumptions due to outliers or inaccurate estimation etc.., then this phenomenon is called uncertainty. In such a case you are unsure about which probabilistic model you have resulting an unknown probability.

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Generally used Symbol for unknown value is $x$ and other letters.

and

unknown probability of some event $A$ is denoted as $P(A)$ or $P_A$.

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You might want to borrow notations from outside mathematics if there is none which suits you. Here are some suggestions: A practical notation for the unknown is the single or triple interrogation mark "?" / "???", as you might use in a table or a database. Sometimes the asterisk "*" is used for similar ends (but note its other uses, which are semantically slightly different from the notion of "unknown": in programming, in regular expressions for example, the asterisk stands as a type of "wild card" for one or more unspecified values, e.g. "night*" for {night, nights, nightly, etc.}; in linguistics it designates a hypothetical, reconstructed word form, such as "*nókʷt-s" for the "night" in Proto-Indo-European). In epigraphy and related sciences the bracketed ellipsis "[...]" stands for an unknown textual sequence, but the notation is more widely known from partial quotes: "Bla bla [...] bla bla."

@egreg: Thanks for the comment - I modified the post accordingly. The point is that if @Igäria Mnagarka really needs a symbol for "unknown" and there is none, it could be invented or borrowed from where it exists.

@Igäria Mnagarka: To push things farther, you could specify the type of unknown you wish to speak about (which would be quite interesting to see applied in Bayesian analysis). Following Donald Rumsfeld's typology and the post above, you could use ? for a known unknown, * for a known known (unspecified value from a set of known values), ! for a unknown known (negation of something specified), and [ ] for a unknown unknown.

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X,Y,Z unknown or variable quantities R. Descartes 1637

taken from: Encyclopedia of Math

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One convention of notation is to use symbols from near the end of the alphabet (e.g., $x$, $y$, $z$, $t$ as others have answered) for "unknown" values and symbols from near the beginning of the alphabet (e.g., $a$, $b$, $c$) for "known" or "fixed" values. Of course conventions vary between fields of mathematics.

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This arises often in statistics, for example, the statistical programming language R has two special values: NaN (mentioned in another answer) and NA. This can be taken as NaN Not a number, can be a result of 0/0 and other illegal operations NA Not available, used to represent "Do logically have a value, but we do not know the value" Typical use cases is data from a questionnaire, where some respondent didnt answer one specific question. If he/she did not answer a question of Gender: woman () man (), do not mean (s)he does not have a gender! Or it might be data from some agriculture experiment, where some plot was destroyed by a tractor. Logically, that plot should have some value (kgs harvested), but that year we didnt get to measure it, since it was destroued. So the value is NA. It would be wrong to use the value zero, even if that was the actual quantity harvested! because that informs us only about an accident irrelevant to the research design.

NA respects some kind of three-valued logic, for instance NA or TRUE = TRUE, while NA and TRUE is NA, we do not have information to answer the question! Note also the weird logic of equality: NA == NA have value NA. For arithmetical comparisons we have 4 < NA is NA (The NA we compare to 4 might be 6, in which case we have TRUE, or it might be 2, in case it is FALSE. so we do not know, that is the value is NA).

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