In semantics, "extension" refers to the range of objects or entities in the world that a particular term or expression denotes. Specifically, the extension of a term is the set of all things that fall under that term. For example: - The extension of the term "dog" includes all actual dogs in the world. - The extension of the term "even number" includes all even numbers (like -4, 0, 2, 4, etc.).

Vish is a traditional Indian board game that is played with a set of pieces on a grid-like board, usually made of cloth or wood. The game is often associated with strategy and skill, similar to chess or checkers. The objective typically involves capturing the opponent's pieces or reaching a designated area on the board. The rules and specifics of Vish can vary by region and community, and it may be known by different names in different cultures.

Consilience is a term that refers to the principle of unity of knowledge, suggesting that evidence from independent, unrelated sources can converge to support a particular conclusion or theory. The concept was popularized by the biologist E.O. Wilson in his 1998 book "Consilience: The Unity of Knowledge." In this work, Wilson argues for the integration of information from different fields such as science, humanities, and social sciences to foster a more comprehensive understanding of complex issues.

Occam's razor is a philosophical and methodological principle that suggests that when presented with competing hypotheses or explanations for the same phenomenon, one should favor the one that makes the fewest assumptions. It is often paraphrased as "entities should not be multiplied beyond necessity" or "the simplest explanation is usually the best." The principle is named after the 14th-century Franciscan friar and philosopher William of Ockham, who emphasized simplicity in reasoning.

Underdetermination refers to a situation in philosophy of science and epistemology where the available evidence is insufficient to uniquely determine which of several competing theories or explanations is the correct one. In other words, multiple hypotheses can explain the same set of observations or data, leading to the conclusion that the evidence does not definitively support one theory over another.

Size theory is a concept used in various fields, including mathematics, physics, and philosophy, but it can vary significantly based on context. Here are some interpretations of "size theory" in different disciplines: 1. **Mathematics**: In mathematical contexts, size theory can refer to concepts related to the measure and dimension of sets, particularly in geometry and topology. It may deal with how different dimensions and sizes of objects can be understood and compared.

We ust use the if mod notation definition as mentioned at: math.stackexchange.com/questions/4305972/what-exactly-is-a-collatz-like-problem/4773230#4773230

Mnemonic: in means into. So we are going into a codomain that is large enough so that we can have a different image for every input.

In this section we classify some functions by the type of inputs and outputs they take and produce.

This is about functions that take functions as input or output.

There's a billion simple looking expressions which are not known to be transcendental numbers or not. It's cute simple to state but hard to prove at its best.

Open as of 2020:

Bibliography:

Homological stability is a concept in algebraic topology and representation theory that deals with the behavior of homological groups of topological spaces or algebraic structures as their dimensions or parameters vary. The basic idea is that for a sequence of spaces \(X_n\) (or groups, schemes, etc.), as \(n\) increases, the homological properties of these spaces become stable in a certain sense.