tag:blogger.com,1999:blog-8534564897606473429.post8717852901395827630..comments2023-10-16T07:01:26.559-07:00Comments on ~ Addo, ergo sum ~: Tangibility of the transcendentalMariusz Popieluchhttp://www.blogger.com/profile/09285082217039015347noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-8534564897606473429.post-72775618381563142462010-05-27T04:22:29.283-07:002010-05-27T04:22:29.283-07:00I had a second look at it, and you're right! I...I had a second look at it, and you're right! If I don't restrict x to Z+ then we could have another x satisfying the equality eg:<br /><br />ceiling(447/10^3)=1<br /><br />and <br /><br />ceiling(447/10^3.2)=1<br /><br />So indeed x wouldn't be unique.Mariusz Popieluchhttps://www.blogger.com/profile/09285082217039015347noreply@blogger.comtag:blogger.com,1999:blog-8534564897606473429.post-28484851841879118882010-05-27T00:06:48.669-07:002010-05-27T00:06:48.669-07:00You're right that a specification of the range...You're right that a specification of the range of Lambda could be given. I actually initially included that specification. But notice that restricting the range of Lambda to non-negative integers forces the domain to be a subset of N. Hence specifying x to be a positive integer is redundant. Notice that for each y there's a unique x satisfying the definition. Having said that I will take your advice and add the redundant restriction for clarity.<br /><br />What I have to fix though is the restriction on the range to exclude zero (Z+) since there is no x such that ceiling(0/10^x)=1.<br /><br />Thanks for the comment Nick. Hope the thesis is coming along well(?).Mariusz Popieluchhttps://www.blogger.com/profile/09285082217039015347noreply@blogger.comtag:blogger.com,1999:blog-8534564897606473429.post-70033937593566657612010-05-26T15:22:32.714-07:002010-05-26T15:22:32.714-07:00Your notation is a little confusing. It looks to m...Your notation is a little confusing. It looks to me that you define the value of the function lambda evaluated at some natural number y to be a set, in particular the set of all x such that the ceiling of y/(10^x) is equal to 1. <br /><br />So for Lambda(1), we obtain all values of x such that ceil[ 1/(10^x)]=1. This is then clearly all non-negative x (if we restrict allowable values of x to the integers, which you should specify).Iterationnoreply@blogger.com