nerocases.blogg.se - Infimum infinitesimals

Infimum infinitesimals software#
Infimum infinitesimals code#
Infimum infinitesimals series#

If we could, then Ω would itself be a limit ordinal and possess a successor ordinal, Ω + 1, which cannot be an element of Ω due to the Axiom of Foundation. You might be forgiven for thinking that we can form a set Ω of all ordinals, but unfortunately this is not the case. All proper classes are subclasses of V, some of which we shall explore: For instance, we cannot have a set of all sets, but we can have a proper class of all sets, namely the von Neumann universe. It transpires that we can get ‘sets’ which are too large to be actual sets, and these are called proper classes. Naturally, it would be improper for me to prematurely release the results, so you’ll have to wait until they appear on Joseph Myers’ website.Īnyway, Cantor first proved that there are multiple distinct infinite cardinals (infinite sets that cannot be bijected), such as the naturals and reals, which are countable and uncountable, respectively. This link runs a test suite in your browser.I apologise for the sporadicity of recent cp4space posts, but I do have several legitimate excuses (including MOG marking, which occupied a significant portion of yesterday). Alternatively, you can access it via a web browser or git, at via github. Modules pointed to from the html source code, but you can view those through your browser as well by pointing it at each

Infimum infinitesimals code#

You can see the source code simply by doing "view source" in your browser actually most of the code is in separate Since it's all written in client-side javascript,

Infimum infinitesimals software#

Inf is open source software by Ben CrowellĪnd Mustafa Khafateh. It may also be possible to accomplish this using control-P and control-N.

In Firefox, you can use up-arrow and down-arrow to get back lines you've typed in previously.

array - converts a Levi-Civita number, complex number, or rational number to a representation in terms of an array.

floor, ceil - round down or up to an integer.

= - assigns the expression on the right to the variable named on the left-hand side.

- separates multiple statements on the same line.

precision - sets the number of digits of precision to print in output.

Infimum infinitesimals series#

levi_civita_n - sets the number of terms to maintain in series expansions of Levi-Civita numbers.

However, the hyperreals cannot be conveniently represented on a computer. The hyperreals match the properties of the real numbers even better than the Levi-Civita numbers do.įor example, the exponential function can take a positive infinite argument in the hyperreal system, but that doesn't work in the Levi-Civita Which were defined by Abraham Robinson around 1960. The undefined result for exp(1/d) is an example of how the Levi-Civita numbers are a smaller system than the hyperreals, Solutions, we arbitrarily pick one and call it d.

().Īssuming such a solution, which is interpreted as an infinitesimal number, it follows that we can find.

, = - comparisons (note the double equals sign to test for equality).

pi - the ratio of a circle's circumference to its diameter.

d - an infinitesimally small positive number.

Inf is a calculator that can handle infinite and infinitesimal numbers.