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I can't believe I spent half my day painting what's basically a shitpost 😅 https://t.co/EYEhz8KC5J
safe (1521768) artist:amarynceus (456) princess luna (91603) twilight sparkle (274100) alicorn (183640) classical unicorn (3656) pony (796411) unicorn (242601) adorkable (2873) chalk (504) chalkboard (2492) cloven hooves (8292) cute (167089) dappled (389) dork (3072) ear fluff (21152) female (846048) freckles (23699) heart (41249) holiday (15327) lesbian (88933) mare (386732) math (762) nerd (737) shipping (176805) text (46220) twilight sparkle (alicorn) (110933) twiluna (1574) unshorn fetlocks (20931) valentine's day (3063)


Syntax quick reference: *bold* _italic_ [spoiler]hide text[/spoiler] @code@ +underline+ -strike- ^sup^ ~sub~
18 comments posted
Background Pony #9CA5
I can't believe I spent half my day painting what's basically a shitpost

Yeah me neither.
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Background Pony #9F66
Also, the equation that is in twi's shadow( her head) deals with bijectiveness in the composition of functions.
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Background Pony #9F66
@Frustration in Excelsis
Onto is not that each element is paired with atleast another element. Onto is where the whole of the codomain is used by the function.

I.E. suppose you have two sets, A = {a,b,c,d} and B = {1,2,3,4}. A bijection here would be something like: f:A → B such that f(a) = 1, f(b) = 2, f© = 3, f(d) = 4. Such a function is a bijection because the whole of the codomain, B, is used by the function and each element has one and only one image( F sends the elements of A to only one element of B). Like all things in upper mathematics, the devil is in the details.

The equations that are there simply re-iterate the definition of a bijection.

The first states that: For every a, a' that exist in A, if f(a) = f(a'), then a = a', which is the definition of an injection. Note that a and a' are two different elements, this is trivial if they are the same element.

The second states that if b is an element of B, then there exists an element, a, that is in A such that f(a) = b. This is the definition of a surjection.

I took mathematics as my first bachelor's degree.
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Frustration in Excelsis
Notoriously Divine Tagger - Consistently uploads images above and beyond the minimum tag requirements. And/or additionally, bringing over the original description from the source if the image has one. Does NOT apply to the uploader adding several to a dozen tags after originally uploading with minimum to bare tagging.
Artist -
Cool Crow - "Caw!" An awesome tagger
Magnificent Metadata Maniac -

Worldbuilding Addict
I did a bit of research, because I was equally confused, and a bijective function is any system where two sets exist, each element of those sets is paired with an element from the other set, and each element is paired with only one element from the other set.

In technical terms, such a function is described as being one-to-one (each element is paired with no more than one other element) and onto (each element is paired with at least one other element).

It's a very dorky way of saying that there's no one but Luna for Twilight.