---
title: cardinality — school dictionary · trees and pragmatics
description: «cardinality» in the school dictionary: The number of things in a set or group. Every meaning for a pupil with its dependency tree and pragmatics.
---

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# cardinality

<!-- .vintro -->
**Who acts:** you, idea, many, cardinality, Two sets, empty set · **What happens:** say, count, tell, be, have · **To what, where:** last number, you, all, 4, apples, 5 · **Speech:** someone speaks here

<!-- .vabout -->
«cardinality» in the school dictionary: its 2 meanings for a pupil and its 5 examples, every sentence parsed by Mova itself — its syntax tree, a dependency tree in the style of Universal Dependencies, and its pragmatics clause by clause. The word in the dictionary, with its sense in the lessons: [cardinality in the school dictionary](https://md.mova.elamur.ai/free/en/dictionaries/school/w/cardinality.md).

## Meaning 1 {#m1}

<!-- .note -->
Usage: maths — kept apart, not parsed.

<!-- .ven lang=en -->
The number of things in a set or group.

```conllu
# sent_id = dict:school:cardinality:m1:1
# text = The number of things in a set or group.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	number	number	NOUN	NN	Number=Sing	0	root	_	_
3	of	of	ADP	IN	_	4	case	_	_
4	things	thing	NOUN	NNS	Number=Plur	2	nmod	_	_
5	in	in	ADP	IN	_	7	case	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	set	set	NOUN	NN	Number=Sing	4	nmod	_	_
8	or	or	CCONJ	CC	_	9	cc	_	_
9	group	group	NOUN	NN	Number=Sing	7	conj	_	SpaceAfter=No
10	.	.	PUNCT	.	_	2	punct	_	_
```

<!-- .note -->
The frames reader finds no event or fact in this sentence.

## Meaning 2 {#m2}

<!-- .note -->
Usage: maths, counting — kept apart, not parsed.

<!-- .ven lang=en -->
The idea that the last number you say when counting tells you how many there are in all.

<!-- fold The tree, 18 words -->
```conllu
# sent_id = dict:school:cardinality:m2:1
# text = The idea that the last number you say when counting tells you how many there are in all.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	idea	idea	NOUN	NN	Number=Sing	11	nsubj	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	last	last	ADJ	JJ	Degree=Pos	6	amod	_	_
6	number	number	NOUN	NN	Number=Sing	11	nsubj	_	_
7	you	you	PRON	PRP	Case=Nom|Person=2|PronType=Prs	8	nsubj	_	_
8	say	say	VERB	VBP	Mood=Ind|Number=Sing|Person=2|Tense=Pres|VerbForm=Fin	6	acl:relcl	_	_
9	when	when	ADV	WRB	PronType=Int	10	advmod	_	_
10	counting	count	VERB	VBG	Tense=Pres|VerbForm=Part	8	advcl	_	_
11	tells	tell	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	root	_	_
12	you	you	PRON	PRP	Case=Acc|Person=2|PronType=Prs	11	iobj	_	_
13	how	how	ADV	WRB	PronType=Int	14	advmod	_	_
14	many	many	ADJ	JJ	Degree=Pos	16	nsubj	_	_
15	there	there	PRON	EX	PronType=Dem	16	expl	_	_
16	are	be	VERB	VBP	Mood=Ind|Number=Plur|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
17	in	in	ADP	IN	_	18	case	_	_
18	all	all	DET	DT	PronType=Tot	16	obl	_	SpaceAfter=No
19	.	.	PUNCT	.	_	11	punct	_	_
```

<!-- .fr -->
| # | verb | tense, mood | who | what, whom | to whom | where | when | other | roles by |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | **say** *speech: assert* | present | you | the last number *not said here* |  |  |  |  | vn say-37.7-1-1 «NP V NP.topic»: agent=Agent number=Topic |
| 2 | **count** | gerund | you *not said here* |  |  |  |  |  | vn matter-91 «NP V»: agent=Stimulus |
| 3 | **tell** *speech: assert* | present | the idea |  | you |  |  |  | vn transfer\_mesg-37.1.1-1-1 «NP V NP S\_INF»: agent=Agent you=Recipient clause=Topic |
| 4 | **be** | present | many |  |  | all; there |  |  | vn exist-47.1 «NP V PP.location»: agent=Theme in all=Location |

## Example 1 {#x1}

<!-- .ven lang=en -->
The cardinality of the set {2, 4, 6, 8} is 4.

<!-- fold The tree, 13 words -->
```conllu
# sent_id = dict:school:cardinality:x1:1
# text = The cardinality of the set {2, 4, 6, 8} is 4.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	cardinality	cardinality	NOUN	NN	Number=Sing	16	nsubj	_	_
3	of	of	ADP	IN	_	5	case	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	set	set	NOUN	NN	Number=Sing	2	nmod	_	_
6	{	{	SYM	SYM	_	7	case	_	SpaceAfter=No
7	2	2	NUM	CD	NumForm=Digit|NumType=Card	5	nmod	_	SpaceAfter=No
8	,	,	PUNCT	,	_	9	punct	_	_
9	4	4	NUM	CD	NumForm=Digit|NumType=Card	7	flat	_	SpaceAfter=No
10	,	,	PUNCT	,	_	11	punct	_	_
11	6	6	NUM	CD	NumForm=Digit|NumType=Card	7	flat	_	SpaceAfter=No
12	,	,	PUNCT	,	_	14	punct	_	_
13	8	8	NUM	CD	NumForm=Digit|NumType=Card	14	nummod	_	SpaceAfter=No
14	}	}	NOUN	NN	Number=Sing	2	conj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	cop	_	_
16	4	4	NUM	CD	NumForm=Digit|NumType=Card	0	root	_	SpaceAfter=No
17	.	.	PUNCT	.	_	16	punct	_	_
```

<!-- .fr -->
| # | verb | tense, mood | who | what, whom | to whom | where | when | other | roles by |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | **is a** | present | the cardinality of the set { 2 and 8 } | 4 |  |  |  |  | tree rules |

## Example 2 {#x2}

<!-- .ven lang=en -->
Count the apples: 1, 2, 3, 4, 5 — the cardinality is 5.

<!-- fold The tree, 12 words -->
```conllu
# sent_id = dict:school:cardinality:x2:1
# text = Count the apples: 1, 2, 3, 4, 5 — the cardinality is 5.
1	Count	count	VERB	VB	Mood=Imp|VerbForm=Fin	0	root	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	apples	apple	NOUN	NNS	Number=Plur	1	obj	_	SpaceAfter=No
4	:	:	PUNCT	:	_	5	punct	_	_
5	1	1	NUM	CD	NumForm=Digit|NumType=Card	3	appos	_	SpaceAfter=No
6	,	,	PUNCT	,	_	7	punct	_	_
7	2	2	NUM	CD	NumForm=Digit|NumType=Card	5	flat	_	SpaceAfter=No
8	,	,	PUNCT	,	_	9	punct	_	_
9	3	3	NUM	CD	NumForm=Digit|NumType=Card	5	conj	_	SpaceAfter=No
10	,	,	PUNCT	,	_	11	punct	_	_
11	4	4	NUM	CD	NumForm=Digit|NumType=Card	5	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	_	13	punct	_	_
13	5	5	NUM	CD	NumForm=Digit|NumType=Card	5	conj	_	_
14	—	-	PUNCT	:	_	18	punct	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	cardinality	cardinality	NOUN	NN	Number=Sing	18	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	cop	_	_
18	5	5	NUM	CD	NumForm=Digit|NumType=Card	1	parataxis	_	SpaceAfter=No
19	.	.	PUNCT	.	_	1	punct	_	_
```

<!-- .fr -->
| # | verb | tense, mood | who | what, whom | to whom | where | when | other | roles by |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | **count** | imperative | you *not said here* | the apples |  |  |  |  | vn multiply-108 «NP V NP»: agent=Agent apple=Theme |
| 2 | **is a** | present | the cardinality | 5 |  |  |  |  | tree rules |

## Example 3 {#x3}

<!-- .ven lang=en -->
Two sets with the same cardinality have the same number of members.

```conllu
# sent_id = dict:school:cardinality:x3:1
# text = Two sets with the same cardinality have the same number of members.
1	Two	two	NUM	CD	NumForm=Word|NumType=Card	2	nummod	_	_
2	sets	set	NOUN	NNS	Number=Plur	7	nsubj	_	_
3	with	with	ADP	IN	_	6	case	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	same	same	ADJ	JJ	Degree=Pos	6	amod	_	_
6	cardinality	cardinality	NOUN	NN	Number=Sing	2	nmod	_	_
7	have	have	VERB	VBP	Mood=Ind|Number=Plur|Person=3|Tense=Pres|VerbForm=Fin	0	root	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	same	same	ADJ	JJ	Degree=Pos	10	amod	_	_
10	number	number	NOUN	NN	Number=Sing	7	obj	_	_
11	of	of	ADP	IN	_	12	case	_	_
12	members	member	NOUN	NNS	Number=Plur	10	nmod	_	SpaceAfter=No
13	.	.	PUNCT	.	_	7	punct	_	_
```

<!-- .fr -->
| # | verb | tense, mood | who | what, whom | to whom | where | when | other | roles by |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | **have** | present | Two sets with the same cardinality | the same number of members |  |  |  |  | vn birth-28.2-1 «NP V NP»: agent=Agent number=Patient |

## Example 4 {#x4}

<!-- .ven lang=en -->
The empty set has cardinality 0.

```conllu
# sent_id = dict:school:cardinality:x4:1
# text = The empty set has cardinality 0.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	empty	empty	ADJ	JJ	Degree=Pos	3	amod	_	_
3	set	set	NOUN	NN	Number=Sing	4	nsubj	_	_
4	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	root	_	_
5	cardinality	cardinality	NOUN	NN	Number=Sing	4	obj	_	_
6	0	0	NUM	CD	NumForm=Digit|NumType=Card	5	flat	_	SpaceAfter=No
7	.	.	PUNCT	.	_	4	punct	_	_
```

<!-- .fr -->
| # | verb | tense, mood | who | what, whom | to whom | where | when | other | roles by |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | **have** | present | the empty set | cardinality |  |  |  |  | vn birth-28.2-1 «NP V NP»: agent=Agent cardinality=Patient |

## Example 5 {#x5}

<!-- .ven lang=en -->
What is the cardinality of the set of days in a week? It is 7.

<!-- .note -->
*Sentence 1:* What is the cardinality of the set of days in a week?

```conllu
# sent_id = dict:school:cardinality:x5:1
# text = What is the cardinality of the set of days in a week?
1	What	what	PRON	WP	PronType=Int	0	root	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	1	cop	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	cardinality	cardinality	NOUN	NN	Number=Sing	1	nsubj	_	_
5	of	of	ADP	IN	_	7	case	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	set	set	NOUN	NN	Number=Sing	4	nmod	_	_
8	of	of	ADP	IN	_	9	case	_	_
9	days	day	NOUN	NNS	Number=Plur	7	nmod	_	_
10	in	in	ADP	IN	_	12	case	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	week	week	NOUN	NN	Number=Sing	9	nmod	_	SpaceAfter=No
13	?	?	PUNCT	.	_	1	punct	_	_
```

<!-- .fr -->
| # | verb | tense, mood | who | what, whom | to whom | where | when | other | roles by |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | **is a** | present | the cardinality of the set of days in a week |  |  |  |  |  | tree rules |

<!-- .note -->
*Sentence 2:* It is 7.

```conllu
# sent_id = dict:school:cardinality:x5:2
# text = It is 7.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	cop	_	_
3	7	7	NUM	CD	NumForm=Digit|NumType=Card	0	root	_	SpaceAfter=No
4	.	.	PUNCT	.	_	3	punct	_	_
```

<!-- .fr -->
| # | verb | tense, mood | who | what, whom | to whom | where | when | other | roles by |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | **is a** | present | cardinality | 7 |  |  |  |  | tree rules |

<!-- div src -->

**Text:** the school dictionary of Mova's schools (`world/data/dictionary-schools/`), written for Mova. **Trees:** Mova's own parse — the `en` model on the CPU, when the site is built — not checked by a teacher; they may be wrong. **Frames:** Mova's frames reader (`prag`), each meaning and example read on its own. Elamur Cosmic License.

<!-- /div -->

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