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originally posted by: Kashai
a reply to: chr0naut
"A dimension in science and mathematics has no thickness."
originally posted by: OpenMindedPhilosopher
a reply to: intrptr
Would it be possible for something to go from 2D to 3D? Something that had no depth to begin with. I don't know just an interesting thought I had I don't know much of anything on the topic.
originally posted by: Kashai
a reply to: chr0naut
In mathematics and science Dimensions define the physical parameters of our existence.
We have thickness and a good reason for that are dimensions.
Can you elaborate on that comment?
Specifically I am referring to this comment...
"A dimension in science and mathematics has no thickness."
Infinitary logic
An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In particular, infinitary logics may fail to be compact or complete. Notions of compactness and completeness that are equivalent in finitary logic sometimes are not so in infinitary logics. Therefore for infinitary logics, notions of strong compactness and strong completeness are defined. This article addresses Hilbert-type infinitary logics, as these have been extensively studied and constitute the most straightforward extensions of finitary logic. These are not, however, the only infinitary logics that have been formulated or studied.
Considering whether a certain infinitary logic named Ω-logic is complete promises[citation needed] to throw light on the continuum hypothesis.
originally posted by: Kashai
a reply to: chr0naut
So simple it is irrelevant to this discussion.
Infinitary logic
An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In particular, infinitary logics may fail to be compact or complete. Notions of compactness and completeness that are equivalent in finitary logic sometimes are not so in infinitary logics. Therefore for infinitary logics, notions of strong compactness and strong completeness are defined. This article addresses Hilbert-type infinitary logics, as these have been extensively studied and constitute the most straightforward extensions of finitary logic. These are not, however, the only infinitary logics that have been formulated or studied.
Considering whether a certain infinitary logic named Ω-logic is complete promises[citation needed] to throw light on the continuum hypothesis.
en.wikipedia.org...
originally posted by: chr0naut
a reply to: King Seesar
Currently, M-Theory has been calculated to require ten dimensions (and upward) to model physical forces properly.
Definitely it doesn't seem to stop at eight.