To’plam tushunchasi. To’plamning elementi

Sonli oraliq	Bеlgilanishi	Tasvirlanishi
Nomlanishi
	(a, b)		Intеrval
	[a, b]		Kеsma
	[a, b)		Yarim intеrval yoki yarim kеsma
	(a, b]		Yarim intеrval yoki yarim kеsma
			Ochiq nur
			Nur yoki yarim to’g’ri chiziq
			Ochiq nur
			Nur

3. Eyler -Venn diagrammalari.
To‘plamlarni geometrik nuqtai nazardan yaqqol ko‘z oldiga keltirish uchun, ular doiracha ko‘rinishida belgilanadi. Masalan: to‘plam to‘plamning xususiy to‘plam osti ekanligi quyidagi ko‘rinishda tasvirlanadi.



Umumiy qismga ega bo’lgan to’plamlar kesishadi deyiladi va
A B = , ya’ni A va B to’plamlar kesishmasi bo’sh emas, deb yoziladi. Masalan, 2 ga karrali natural sonlar va 5 ga karrali natural sonlar to’plamlari umumiy elementga ega, ya’ni kesishadi yoki kesishmasi bo’sh emas. Bu to’plamlar kesishmasi barcha 10 ga karrali natural sonlardan iborat bo’ladi.
Ikki to’plamning o’zaro munosabatida to’rt hol bo’lishi mumkin (I.2-rasm):

1. 
   to’plamlar kesishmaydi (I.2-rasm, 1);
   
2. 
   to’plamlar kesishadi (I.2-rasm, II);
   
3. 
   to’plamning biri ikkinchisining qismi bo’ladi(I.2-rasm, III);
   
4. 
   to’plamlar ustma-ust tushadi, ya’ni teng (I.2-rasm, IV).
   

Elementar munosabatlar

To`plamlar bilan ishlaganda, “x ni A to`plamning elementi deb hisoblaymiz, shu narsa o`rinliki va bu tasdiq quydagicha belgilanadi x A. Shunday qilib, agar Z butun sonlar to`plami bo`lsa biz quyidagi tasdiqlarni yozishimiz mumkin 3 Z, -11 Z, va hokazo. Bundan tashqari butun son emas, shuning uchun biz uni quyidagicha yozamiz _Z⁷.
Elementary relationships
When dealing with sets nai vely ,we shall assume that the statement “x in an element of the set A”makes sens and shall symbolically denote this stastment by writing x A.Thus, if Z denotes the set of integers , we can write such statements as 3 Z ,-11 Z ,and so on. Likewise, is not an integer so we’ll express this by writing Z .
In the vast majority of our considerations we shall be considering sets in a given “context”, i..e..,as subsets of a given set. thus ,when I speak of the set of integers ,I am usually referring to a particular subset of the real numbers .The point here is that while we might not really know what a real number is (and therefore we don’t really “understand” the set of real numbers ),we probably have a better understanding of the particular subset consisting of integers (whole numbers ).Anyway ,if we denote by R the set of all real numbers and write Z for the subset of of integers ,then we can say that.
Mustaqil o’rganish uchun savоllar

1. 
   To‘plam deganda nimani tushunasiz?
   
2. 
   Bo‘sh, chekli, cheksiz to‘plamlarga misollar keltiring.
   
3. 
   To‘plamlar necha xil usulda beriladi?
   
4. 
   Teng to‘plamlarga ta’rif bering.
   
5. 
   To‘plam osti tushunchasiga ta’rif bering va misollar keltiring.
   
6. 
   Qanday to‘plamlar ekvivalent to‘plamlar deyiladi va qanday qilib ikki to‘plam orasida ekvivalentlikni o‘rnatish mumkin.
   
7. 
   Universal to‘plam deganda qanday to‘plamni tushunasiz? Misollar keltiring.