immeasurable
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we often use capital omega, Ω to mean "the whole set"
Ω = "all"
"Do I not fill the heavens and the earth?" declares the LORD.
(Jeremiah 23:24)
(Jeremiah 23:24)
therefore,
Yah ≥ Ω
the heavens and the highest heavens cannot contain Him
(2 Chronicles 2:6)
(2 Chronicles 2:6)
therefore,
Yah > Ω
. . . you might say He is 'a special case' -- "to be treated separately"
"holy" means literally, "separated" or "set apart"
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i find this extraordinarily interesting --
And he measured the wall thereof, an hundred and forty and four cubits,
according to the measure of a man, that is, of the angel.
(Revelation 21:17)
angelic measure = human measure?
... maybe so ...
but it also implies, this is not the only measure or else it wouldn't be necessary to say 'which measure' is being used ((!!!))
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Psalm 36:5-9
Thy mercy, O LORD, is in the heavens; and thy faithfulness reacheth unto the clouds.
6Thy righteousness is like the great mountains; thy judgments are a great deep: O LORD, thou preservest man and beast.
7How excellent is thy lovingkindness, O God! therefore the children of men put their trust under the shadow of thy wings.
8They shall be abundantly satisfied with the fatness of thy house; and thou shalt make them drink of the river of thy pleasures.
9For with thee is the fountain of life: in thy light shall we see light.
Thy mercy, O LORD, is in the heavens; and thy faithfulness reacheth unto the clouds.
6Thy righteousness is like the great mountains; thy judgments are a great deep: O LORD, thou preservest man and beast.
7How excellent is thy lovingkindness, O God! therefore the children of men put their trust under the shadow of thy wings.
8They shall be abundantly satisfied with the fatness of thy house; and thou shalt make them drink of the river of thy pleasures.
9For with thee is the fountain of life: in thy light shall we see light.
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Singularity
From Wikipedia, the free encyclopedia
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Look up Singularity or singularity in Wiktionary, the free dictionary.
Singularity or singular point may refer to:
Contents
Science, technology, and mathematics[edit]
Mathematics[edit]
From Wikipedia, the free encyclopedia
Jump to navigationJump to search
Singularity or singular point may refer to:
Contents
Science, technology, and mathematics[edit]
Mathematics[edit]
- Mathematical singularity, a point at which a given mathematical object is not defined or not "well-behaved", for example infinite or not differentiable
- Singular point of a curve, where the curve is not given by a smooth embedding of a parameter
- Singular point of an algebraic variety, a point where an algebraic variety is not locally flat
- Rational singularity
- Essential singularity, a singularity near which a function exhibits extreme behavior
- Isolated singularity, a mathematical singularity that has no other singularities close to it
- Movable singularity, a concept in singularity theory
- Removable singularity, a point at which a function is not defined but at which it can be so defined that it is continuous at the singularity
- Singularity (system theory), in dynamical and social systems, a context in which a small change can cause a large effect
- Gravitational singularity, a region in spacetime in which tidal gravitational forces become infinite
- Initial singularity, a hypothesized singularity of infinite density before quantum fluctuations caused the Big Bang and subsequent inflation that created the Universe
- Penrose–Hawking singularity theorems, theorems in general relativity theory about when gravitation produces singularities such as black holes
- Prandtl–Glauert singularity, the point at which a sudden drop in air pressure occurs
- Singularity (climate), a weather phenomenon associated with a specific calendar date
- Van Hove singularity in the density of states of a material
- Singularity (operating system), an operating system developed by Microsoft Research written in managed code
- Mechanical singularity, a position or configuration of a mechanism or a machine where the subsequent behavior cannot be predicted
- Technological singularity, a hypothetical moment in time when any physically conceivable level of technological advancement is attained instantaneously
- Singularity (software), a container technology that does not require root permissions to run
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yes, many measures, and many ways to be immeasurable.
the mathematical definition of measure is a little complicated, it takes defining several terms of the definition too. i thought maybe too complex to post for now. but to try to explain it 'simply' it is the smallest cover of a set -- where a 'cover' is a collection of non-overlapping (("disjoint")) sets that, if you add them all together, account for an whole set. think of a bed that you are trying to make a quilt for, any cover is an arrangement of possible quilt pieces that don't overlap and don't leave any gaps between them, and cover up the whole bed. it could be too big, or be just the right size. the smallest possible one that covers the whole bed is the 'measure' -- which is of course a really shoddy analogy and it's more technical than that.. but it's a start.
so, one way to be immeasurable is for there to be no way to not leave gaps.
another way is if there is no way to not leave some part of the bed not covered up -- like you can't make the quilt big enough
another way is if it is not possible not to overlap
'uncountable' is another word that has a special meaning in math that may not be intuitive. it means you can't map something in a 1:1 & onto way to the positive integers. there are a number of ways something can be uncountable, and there are many infinite things that are 'countable'
another way to be immeasurable is to have only uncountable covers.
.. .but i don't want this thread to get too technical yet. we'll get lost lol.. and i probably will too; i haven't actually had a measure theory class yet, tho when i eventually go back to finish, it's the one thing i know i really want to learn.
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in a few of the verses on page 1, God is also described qualitatively immeasurable/unsearchable -- for example ((actually i don't think i posted this one yet?))
not trying to be too technical at this point, i'm lumping 'unsearchable' and 'uncountable' and 'immeasurable' all together as one set of very similar things; maybe at some point i'll feel confident about differentiating
the mathematical definition of measure is a little complicated, it takes defining several terms of the definition too. i thought maybe too complex to post for now. but to try to explain it 'simply' it is the smallest cover of a set -- where a 'cover' is a collection of non-overlapping (("disjoint")) sets that, if you add them all together, account for an whole set. think of a bed that you are trying to make a quilt for, any cover is an arrangement of possible quilt pieces that don't overlap and don't leave any gaps between them, and cover up the whole bed. it could be too big, or be just the right size. the smallest possible one that covers the whole bed is the 'measure' -- which is of course a really shoddy analogy and it's more technical than that.. but it's a start.
so, one way to be immeasurable is for there to be no way to not leave gaps.
another way is if there is no way to not leave some part of the bed not covered up -- like you can't make the quilt big enough
another way is if it is not possible not to overlap
'uncountable' is another word that has a special meaning in math that may not be intuitive. it means you can't map something in a 1:1 & onto way to the positive integers. there are a number of ways something can be uncountable, and there are many infinite things that are 'countable'
another way to be immeasurable is to have only uncountable covers.
.. .but i don't want this thread to get too technical yet. we'll get lost lol.. and i probably will too; i haven't actually had a measure theory class yet, tho when i eventually go back to finish, it's the one thing i know i really want to learn.
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in a few of the verses on page 1, God is also described qualitatively immeasurable/unsearchable -- for example ((actually i don't think i posted this one yet?))
Behold, God is exalted, and we do not know Him; The number of His years is unsearchable.
(Job 36:26)
(Job 36:26)
not trying to be too technical at this point, i'm lumping 'unsearchable' and 'uncountable' and 'immeasurable' all together as one set of very similar things; maybe at some point i'll feel confident about differentiating
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this is only one measure in the mathematical sense.
a minimum open cover of a set is not the only measure -- but maybe easiest way to understand. like tiling a bathroom floor; infinite number of ways to cut pieces of tile, but one total area of the floor: the area is the 'measure' of the floor. this is just one basic, intuitive measure; by no means the only one, and not strictly the definition of 'measure' but an example of one.
ex. you can define a measure as the smallest number of tiles you can use, or the smallest total length of grout between all the individual tiles. you could define one as the circumference, or the longest diagonal, or many other ways.
this is only one measure in the mathematical sense.
a minimum open cover of a set is not the only measure -- but maybe easiest way to understand. like tiling a bathroom floor; infinite number of ways to cut pieces of tile, but one total area of the floor: the area is the 'measure' of the floor. this is just one basic, intuitive measure; by no means the only one, and not strictly the definition of 'measure' but an example of one.
ex. you can define a measure as the smallest number of tiles you can use, or the smallest total length of grout between all the individual tiles. you could define one as the circumference, or the longest diagonal, or many other ways.