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- этимология
Что (кто) такое surjection$530235$ - определение
TYPE OF PROPERTY OF A COLLECTION OF MATHEMATICAL OBJECTS WHICH ARE UNIQUELY DETERMINED BY LESS INFORMATION THAN ONE WOULD EXPECT
Rigidity theorem; Rigid surjection
onto
![range]]) of ''f''. This function is '''not''' surjective, because the image does not fill the whole codomain. In other words, ''Y'' is colored in a two-step process: First, for every ''x'' in ''X'', the point ''f''(''x'') is colored yellow; Second, all the rest of the points in ''Y'', that are not yellow, are colored blue. The function ''f'' would be surjective only if there were no blue points.](https://commons.wikimedia.org/wiki/Special:FilePath/Codomain2.SVG?width=200 "range]]) of ''f''. This function is '''not''' surjective, because the image does not fill the whole codomain. In other words, ''Y'' is colored in a two-step process: First, for every ''x'' in ''X'', the point ''f''(''x'') is colored yellow; Second, all the rest of the points in ''Y'', that are not yellow, are colored blue. The function ''f'' would be surjective only if there were no blue points.")
FUNCTION SUCH THAT EVERY ELEMENT HAS A PREIMAGE
Surjective; Onto; Onto function; Surjectivity; Onto (mathematics); Surjective map; Surjection; ↠; Surjective Function; Induced function; Onto mapping
surjection
FUNCTION SUCH THAT EVERY ELEMENT HAS A PREIMAGE
Surjective; Onto; Onto function; Surjectivity; Onto (mathematics); Surjective map; Surjection; ↠; Surjective Function; Induced function; Onto mapping
<mathematics> A function f : A -> B is surjective or onto or a
surjection if f A = B. I.e. f can return any value in B.
This means that its image is its codomain.
Only surjections have right inverses, f' : B -> A where
f (f' x) = x since if f were not a surjection there would be
elements of B for which f' was not defined.
See also bijection, injection.
(1995-05-27)
onto
FUNCTION SUCH THAT EVERY ELEMENT HAS A PREIMAGE
Surjective; Onto; Onto function; Surjectivity; Onto (mathematics); Surjective map; Surjection; ↠; Surjective Function; Induced function; Onto mapping
also on to
Frequency: The word is one of the 3000 most common words in English.
Note: In addition to the uses shown below, 'onto' is used in phrasal verbs such as 'hold onto' and 'latch onto'.
1.
If something moves or is put onto an object or surface, it is then on that object or surface.
I took my bags inside, lowered myself onto the bed and switched on the TV...
Smear Vaseline on to your baby's skin to prevent soreness.
PREP
2.
You can sometimes use onto to mention the place or area that someone moves into.
The players emerged onto the field...
Alex turned his car on to the Albert Quay and drove along until he found a parking place.
PREP
3.
You can use onto to introduce the place towards which a light or someone's look is directed.
...the metal part of the door onto which the sun had been shining...
...the house with its leafy garden and its view on to Regent's Park.
PREP
4.
You can use onto to introduce a place that you would immediately come to after leaving another place that you have just mentioned, because they are next to each other.
...windows opening onto carved black-wood balconies...
The door opened onto a lighted hallway.
PREP: v PREP n
5.
When you change the position of your body, you use onto to introduce the part your body which is now supporting you.
As he stepped backwards she fell onto her knees, then onto her face...
I willed my eyes to open and heaved myself over on to my back.
PREP
6.
When you get onto a bus, train, or plane, you enter it in order to travel somewhere.
As he got on to the plane, he asked me how I was feeling...
'I'll see you onto the train.'-'Thank you.'
? off
PREP
7.
Onto is used after verbs such as 'hold', 'hang', and 'cling' to indicate what someone is holding firmly or where something is being held firmly.
The reflector is held onto the sides of the spacecraft with a frame...
She was conscious of a second man hanging on to the rail...
PREP
8.
If people who are talking get onto a different subject, they begin talking about it.
Let's get on to more important matters...
So, if we could just move onto something else?
PREP
9.
You can sometimes use onto to indicate that something or someone becomes included as a part of a list or system.
The Macedonian question had failed to get on to the agenda...
The pill itself has changed a lot since it first came onto the market...
Twelve thousand workers will go onto a four-day week at their factory in Birmingham.
PREP
10.
If someone is onto something, they are about to discover something important. (INFORMAL)
He leaned across the table and whispered to me, 'I'm really onto something.'...
Archaeologists knew they were onto something big when they started digging.
PREP: be PREP n
11.
If someone is onto you, they have discovered that you are doing something illegal or wrong. (INFORMAL)
I had told people what he had been doing, so now the police were onto him.
PREP: be PREP n
Википедия
Rigidity (mathematics)
In mathematics, a rigid collection C of mathematical objects (for instance sets or functions) is one in which every c ∈ C is uniquely determined by less information about c than one would expect.
The above statement does not define a mathematical property. Instead, it describes in what sense the adjective rigid is typically used in mathematics, by mathematicians.
