Send
Close Add comments:
(status displays here)
Got it! This site "creationpie.com" uses cookies. You consent to this by clicking on "Got it!" or by continuing to use this website. Note: This appears on each machine/browser from which this site is accessed.
Reflexive properties
1. Reflexive property
A relation
R on set
A is
reflexive if for every
x in
A,
x R x.
This can be written in mathematical form as follows.
This is read as "
for all x in (set) A, (condition) x R x (is true)"
2. Universal quantification
Universal quantification involves "
for all" within a certain domain set.
The symbol "
∀" is read as "
for all".
An example is as follows.
∀ x ∈ { 1 , 3 , 5 } : x is an odd number
This is read as "
for all x in the set 1, 3, 5, x is an odd number"
The symbol "∈" is read as "in" which is short for "is an element of" (the domain set that follows).
The symbol ":" (colon) can be thought of as saying "such that" or "it is true that" (what follows).
3. Reflexive laughing
An example of a
reflexive rule is the following.
It is good to be able to laugh at oneself.
Have you heard that being able to laugh at yourself may help
lengthen your life?
Here, the "
laugh at" relation is applied
reflexively to itself. That is, relating "
laugh at" from "
you" to "
you".
4. Not reflexive laughing
Have you heard that laughing at your spouse may help
shorten your life?
Here, the "
laugh at" relation is not applied reflexively.
5. Laughing summary
Here is the diagram to summarize these laughing ideas.
The relation
R as "
is the same sex/gender as" is reflexive, since
person
x "
is the same sex/gender as" person
x.
Does a rule apply to itself? If so, the rule is reflexive.
6. Self reference
Are you the same sex or gender, whatever that is, as yourself?
Except for negation, most logical (not human) rules are reflexive.
Do some people apply rules to others but not to themselves?
7. Do as I say
Whenever someone says, "
Do as I say, not as I do" they are applying a rule to others but not to them-self. That is, the rule, to them, is not a reflexive rule. In such a case, one might call the person a "
hypocrite" using the modern sense of the word.
8. Everyone do this
The pattern becomes more clear with a diagram. The rule applies to everyone, which includes self. Negation results in interesting ideas.
Math proof that disproves itself (incompleteness)
Halting problem that detects itself halting (incomputability)
Minimal programs that detect randomness
9. End of page
