the cardinality of a set is the number of things in it.
some sets have infinite items in them such as the counting numbers (there’s always a bigger fish dot jpeg). but not all infinities are equal some are larger.
equality: if we can map a 1:1 rule between items in two sets with infinite items they are said to be equal infinities.
greater: but if we can map all in one set to another and note that there are still items left over, the first set has more things in it so if the other set has infinity items in it, this collection must have an even larger set of items in it, a greater tier of infinite.
a common example in math classes is mapping items in the real number between 0 and 1 to the counting numbers (1,2,3,…) using the rule 1>1/1, 2>1/2, 3>1/3,… we can see (0 to 1) has a 1:1 mapping but there are still more items (for instance 1/1.5). this shows there are more items in the real number line from 0 to 1 than there is items in the counting numbers. though both are infinite one infinity is larger.
so the meme. it’s asking you to imagine a collection items that has greater number than the counting number infinity, but less than the next tier of infinity, those in the real number line. something which is hard to imagine because if it were easy we would have plugged that infinity tier into our tiering system.
Batman@lemmy.world 4 weeks ago
the cardinality of a set is the number of things in it.
some sets have infinite items in them such as the counting numbers (there’s always a bigger fish dot jpeg). but not all infinities are equal some are larger.
equality: if we can map a 1:1 rule between items in two sets with infinite items they are said to be equal infinities.
greater: but if we can map all in one set to another and note that there are still items left over, the first set has more things in it so if the other set has infinity items in it, this collection must have an even larger set of items in it, a greater tier of infinite.
a common example in math classes is mapping items in the real number between 0 and 1 to the counting numbers (1,2,3,…) using the rule 1>1/1, 2>1/2, 3>1/3,… we can see (0 to 1) has a 1:1 mapping but there are still more items (for instance 1/1.5). this shows there are more items in the real number line from 0 to 1 than there is items in the counting numbers. though both are infinite one infinity is larger.
so the meme. it’s asking you to imagine a collection items that has greater number than the counting number infinity, but less than the next tier of infinity, those in the real number line. something which is hard to imagine because if it were easy we would have plugged that infinity tier into our tiering system.
MonkderVierte@lemmy.zip 4 weeks ago
Thanks!