Knowledge (XXG)

Subclass (set theory)

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is a subclass of every class, and any class is a subclass of itself. But additionally, every class is a subclass of the class of all sets. Accordingly, the subclass relation makes the collection of all classes into a
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in the collection of all classes. (Of course, the collection of all classes is something larger than even a class!)
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contained in some other set. One may also call this "inclusion of classes".
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contained in some other class in the same way that a
183: 8: 190: 176: 121:. Dover Publications Inc. p. 240. 107: 7: 144: 142: 162:. You can help Knowledge (XXG) by 14: 146: 20:and its applications throughout 1: 230: 141: 115:Charles C.Pinter (2013). 82:must then also be a set. 43:That is, given classes 158:-related article is a 78:essentially says that 76:axiom of specification 85:As with subsets, the 118:A Book of Set Theory 66:is also a member of 171: 170: 55:is a subclass of 221: 214:Set theory stubs 192: 185: 178: 150: 143: 133: 132: 112: 62:every member of 229: 228: 224: 223: 222: 220: 219: 218: 199: 198: 197: 196: 139: 137: 136: 129: 114: 113: 109: 104: 92:Boolean lattice 12: 11: 5: 227: 225: 217: 216: 211: 201: 200: 195: 194: 187: 180: 172: 169: 168: 151: 135: 134: 128:978-0486497082 127: 106: 105: 103: 100: 74:be a set; the 60:if and only if 13: 10: 9: 6: 4: 3: 2: 226: 215: 212: 210: 207: 206: 204: 193: 188: 186: 181: 179: 174: 173: 167: 165: 161: 157: 152: 149: 145: 140: 130: 124: 120: 119: 111: 108: 101: 99: 97: 93: 88: 83: 81: 77: 73: 69: 65: 61: 58: 54: 50: 46: 41: 39: 35: 31: 27: 23: 19: 164:expanding it 153: 138: 117: 110: 84: 79: 71: 67: 63: 56: 52: 48: 44: 42: 25: 15: 22:mathematics 209:Set theory 203:Categories 156:set theory 102:References 18:set theory 87:empty set 26:subclass 125:  34:subset 154:This 96:ideal 36:is a 30:class 28:is a 160:stub 123:ISBN 47:and 24:, a 38:set 16:In 205:: 51:, 191:e 184:t 177:v 166:. 131:. 80:A 72:B 68:B 64:A 57:B 53:A 49:B 45:A

Index

set theory
mathematics
class
subset
set
if and only if
axiom of specification
empty set
Boolean lattice
ideal
A Book of Set Theory
ISBN
978-0486497082
Stub icon
set theory
stub
expanding it
v
t
e
Categories
Set theory
Set theory stubs

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