What if not understanding constructivism is like not having

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>>4947811
>11
I think you need to speak louder and in Italian.

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>>4947811
i don't get it, but

>11
>the double numbers again!
>LEL XDDDDDDDDDDDDD

>>4947827
>In Raymond Smullyan’s story there was a planet on which the concept of humor was unknown and laughter was treated as a disease. Those who laughed were sent to live in laugh-hospitals, away from normal people. As time passed ever more people contracted laughter and the laugh-hospitals grew into whole laugh-communities, until the few remaining normal people pretended to understand humor just so that they could join the rest. What if constructive models are like the laugh-hospitals? What if not understanding constructivism is like not having a sense of humor?
>Apart from sheaves on a space there are many other toposes, each a model of constructive mathematics. They were invented by the great Alexander Grothendieck for the purposes of studying algebraic geometry, but have since proved generally useful in mathematics. The Dubuc topos contains the 17th-century nilpotent infinitesimals, but without the 17th-century confusion and paradoxes. Joyal’s theory of combinatorial species is just a topos in disguise, and so are various kinds of graphs. Simplicial sets, the home of homotopy theorists, form a presheaf topos. The realizability toposes are computer scientists’ Gardens of Eden in which everything is computable by design. Even such mundane topics as the syntax of programming languages get their own toposes.

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>>4947839
Ohhh. So like how if it's assumed that for any mode of existence a method of Perfect Compression exists to accurately model that existence, then this would necessitate only a single solution to its set of coordinates in whatever system is used to model it, since any version of Perfect Compression with additional locations other than the minimum required would therefor be less than optimal compared to the version of Perfect Compression that did not require those additional locations? And how simultaneously no amount of processes (whether geometrically transformational or via symbolic calculus) will ascertain the location of Perfect Compression to a single set of coordinates, because any version with fewer processes other than the maximum possible for Perfect Compression would therefor encode less data and so be less efficient compared to the version of Perfect Compression that encoded more data via those additional processes?

So I guess to those constructivists who seek it, Perfect Compression is simultaneously exactly only in one location, yet always possibly in many. Like that?

>MEMES
>LEL XDDDDDDDDDDDDD

>>4947903
The pigeonhole principle does not imply bijectivity in the infinite case, which is OK since there are only finitely many numbers, if you think about it.
This makes epi mono factorization trivial though.

>>4947811
good quandry my dude

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>>4947928
Is Perfect Compression the algorithm that is efficient for all data sets?

Or is it the algorithm that is infinitely efficient, for even only one data set?

>>4947938
Lossless compression is nothing other than relabeling. You can't win with one data type without losing an equivalent amount in another.
The gains from compression exist because one has a lot of reduncancy information that isn't used in the present representation.

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>>4947955
>the double numbers again

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>>4947827
From the thumbnail it looks like the woman on the right is puking.

>>4947827
>>4947839
>>4947903
>>4947959
Whom are you quoting?

>>4947811
yea the russians sure were on to something when they eliminated representation from art

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E=MC^2