In addition, we occasionally wish to include the infinity (∞) in our discussion, and there is a positive infinity +∞ and a negative infinity −∞. Any number n is less than +∞, that is, n<+∞. Any number is also greater than −∞ (i.e., −∞<n). Therefore, all ...
One can define functions on the ordinals by transfinite induction (which is sometimes also referred to as transfinite recursion). Prior to the formulation of this procedure let us give an auxiliary definition. Given a function F, by means of a functional condition (p. 50), and a set x suc...
We study the Cantor real base numeration system which is a common generalization of two positional systems, namely the Cantor system with a sequence of integer bases and the Rényi system with one real base. We focus on the case of an alternate base BB given by a purely periodic sequence (...
m in a very complicated relationship with another 8 who is a Leo. We communicate very well and understand each other when no one else does. We work really well together and usually we win at everything we start together. Emotionally however, we always hit stumbling blocks. He is very ...
I can’t really imagine the other albums on this list being made prior to the 2020s; if that isn’t true about this one, what is true is that the record proves you can still string together short, dense songs in a way that casts a spell across more than an hour of music. Every...
1 can be written as a product of one or more primes in a way which is unique except possibly for the order of the prime factors. The same prime factor may occur multiple times. Primes can thus be considered the “basic building blocks” of the natural numbers. For example, we can ...
The fraction of the genome allowed to be non-clonal was set to infinity so that the maximum number of solutions could be evaluated. ABSOLUTE returns a set of possible values for ploidy and CCF. The closest solution to that returned by GAP in Euclidean space, after rescaling ploidy values to...
On another note... I think that any arguments which appeal to essential building blocks, and zero being a necessary component, need to consider the importance of -1. In any system of counting which begins with the notion of incremental components, we would be unable to incorporate one of th...
an opaque part of an optical system that blocks certain rays. The aperture stop is the aperture that limits the brightness of the image by restricting the input pupil size, while a field stop is a stop intended to cut out light that would be outside the desired field of view and might ...
The IEEE floating-point standard has special cases to represent numbers such as zero, infinity, and illegal results. For example, representing the number zero is problematic in floating-point notation because of the implicit leading one. Special codes with exponents of all 0’s or all l’s are...