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Suppose there is a people somewhere that has not yet been corrupted by what we like to call civilization.<\/p>\nSuppose there is a people somewhere that has not yet been corrupted by what we like to call civilization.<\/p>\n
Their mathematical skills allow them to count up to five, but not beyond. Anything over 5 is considered ‘many’.<\/p>\n
Does that mean they consider all collections of over 5 items as quantitively equal?<\/p>\n
No, of course not. They fully realize that there are different kinds of ‘many’: a handful of peanuts is not quite as ‘many’ as a bucket full of peanuts!<\/p>\n
Somewhat similarly, ‘civilized’ mathematicians have come to realize that there are different kinds of infinities. Even though we can’t count them, we know that there are infinite sets that differ in ‘size’.<\/p>\n
But things get a bit weird when it comes to infinities.<\/p>\n
Take for instance the infinite set of all integers.<\/p>\n
It’s obvious, and one can also show mathematically, that the set of all EVEN integers is as ‘big’ (or strong) as the set of all ODD integers.<\/p>\n
To get you to think a bit about infinities, I’ll end this short introductory\u00c2\u00a0post\u00c2\u00a0to a (finite!) set of posts on infinities here with a small ‘test’.<\/p>\n
I intend to explain later where I’m going with all this. For now, I’d like to keep it simple.<\/p>\n
Question:
\nLet ‘I’ be the set of all integers, ‘E’ the set of all EVEN integers and ‘S(s)’ the size\u00c2\u00a0 of set ‘s’.
\nWhat can be said about the size of I?<\/p>\n
Answers 1)<\/sup> Bonus question: Suppose there is a people somewhere that has not yet been corrupted by what we like to call civilization. Their mathematical skills allow them to count up to five, but not beyond. Anything over 5 is considered ‘many’. Does that mean they consider all collections of over 5 items as quantitively equal? No, of course […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31],"tags":[],"class_list":["post-129","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"http:\/\/claessen.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/129","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/claessen.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/claessen.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/claessen.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/claessen.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=129"}],"version-history":[{"count":0,"href":"http:\/\/claessen.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/129\/revisions"}],"wp:attachment":[{"href":"http:\/\/claessen.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=129"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/claessen.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=129"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/claessen.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\na. S(I) < S(E)
\nb. S(I) = S(E)
\nc. S(I) > S(E)
\nd. Huh?<\/p>\n
\nWhat is the most dangerous remark in the above post, especially with regards to the correct answer?<\/p>\n\n
\n 1)<\/sup><\/td>\n For the equation challenged:
\nIs the set of all integers a) smaller, b) equal or c)\u00c2\u00a0larger than the set of all even intergers, or d) no clue?<\/font><\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":"