The biggest barrier to approximating i, the imaginary number, as we approximate pi is the lack of a number -1. It is not clear how to take the square root of a negative symbol. <\/p>\n\n\n\n
Interestingly, there are numeric representations of -1 in the left infinite numbers, the numbers that can continue to arbitrary large terms usually written to the left; …111. This has a similarity with real numbers that can continue to arbitrary small terms, usually written to the right; 1.111… <\/p>\n\n\n\n
With these left infinite numbers, the left infinite string of (base -1) is a representation of -1. To see this, consider the example …999 . Adding …999+1 = …99(10) = …9(10)0 = …(10)00 = …000 which is zero. Base 10 can be replaced with any usual base. The import property is the carry.<\/p>\n\n\n\n
This may seem strange, but this concept is used in most computers as the 2s complement representation. This representation uses all 1s to represent negative 1 and takes advantage of the natural arithmetic available.<\/p>\n\n\n\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
The biggest barrier to approximating i, the imaginary number, as we approximate pi is the lack of a number -1. It is not clear how to take the square root of a negative symbol. Interestingly, there are numeric representations of -1 in the left infinite numbers, the numbers that can continue to arbitrary large terms… Continue reading Numeric approximations to the imaginary number: representations of negative numbers<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,5],"tags":[],"class_list":["post-89","post","type-post","status-publish","format-standard","hentry","category-imaginary-number","category-nonfiction","entry"],"_links":{"self":[{"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/posts\/89","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/comments?post=89"}],"version-history":[{"count":3,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/posts\/89\/revisions"}],"predecessor-version":[{"id":101,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/posts\/89\/revisions\/101"}],"wp:attachment":[{"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/media?parent=89"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/categories?post=89"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/tags?post=89"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}