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Combined display of all available logs of Objective Mathematics. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).

• 03:00, 21 July 2024 Lfox talk contribs created page Limits (essay) (Created page with "'''essay prompt''': Is the idea of 'limit' indispensable? Neutral? A hindrance? I contend that some concept of 'limit' is indispensable in mathematics, physics, and beyond. I will make this case inductively, beginning with an exposition of the facts of reality that gave rise to the need for such a concept, and concluding with a proper definition of 'limit'. [TODO maybe also talk about invalid versions of the concept?] == Fact of reality 1: == The Earth is a sphere, bu...") Tag: Visual edit
• 17:22, 8 July 2024 Lfox talk contribs created page E (Created page with "'''e''' is the == Geometric interpretation == thumb|" A ray through the unit hyperbola ''x''² − ''y''² = 1 at the point (cosh ''a'', sinh ''a''), where ''a'' is twice the area between the ray, the hyperbola, and the ''x''-axis. For points on the hyperbola below the ''x''-axis, the area is considered negative" [TODO] <math>\cosh(a)</math> and <math>\sinh(a)</math> are the <math>x</math> and <math>y</...") Tag: Visual edit
• 17:20, 8 July 2024 Lfox talk contribs created page File:1920px-Hyperbolic functions-2.svg.png
• 17:20, 8 July 2024 Lfox talk contribs uploaded File:1920px-Hyperbolic functions-2.svg.png
• 17:25, 3 July 2024 Lfox talk contribs created page Limit (Created page with "The '''limit''' (of a Cauchy procedure) is the target which a Cauchy procedure approaches. [TODO ugh] == Examples == === Planes are the limit of increasingly large spheres === Work with 3 dimensional rectilinear coordinates, and consider some sequence of spheres, <math>C_1, C_2, \cdots </math> on the plane, where the sphere <math>C_n</math> is centered at <math>(0, 0, n) </math> and has radius <math>n</math>. Near the origin <math>(0,0,0)</math>, the sphere <math>C_n</...") Tag: Visual edit
• 16:26, 2 July 2024 Lfox talk contribs created page Magnitude (Created page with "A '''magnitude''' is a quantity with no restriction on how it can be divided into parts.<ref>Aristotle, ''Metaphysics'', Book V, Ch. 11-14</ref>") Tag: Visual edit
• 18:20, 19 June 2024 Lfox talk contribs created page Multitude (Created page with "'''Multitude''' is the quantity of a finite set. Synonyms for multitude are '''natural number''', '''whole quantity''', '''discrete quantity''', '''cardinality''', and the symbol <math>\mathbb{N}</math>; though all those concepts have different shades of meaning, Objective Mathematics uses them interchangeably. == Comparison == "Few" and "many" describe relative multitudes. == Counting == Counting is a process by which one identifies the isomorphism class of...") Tag: Visual edit
• 21:55, 27 May 2024 Lfox talk contribs created page Group (Created page with "[TODO defn] Consider a thing with some symmetry. A symmetry is a transformation of the thing which leaves it unchanged. Technically speaking, == Finite groups == == Infinite groups == == Notes == <references group="note" />") Tag: Visual edit: Switched
• 20:11, 25 April 2024 Lfox talk contribs created page Probability (Created page with "'''Probability''' is a quantitative method of exploiting the symmetry of a system to reach, with certainty, conclusions about aggregates of outcomes, even when each individual outcome is uncertain. The idea is that every context determines some small number <math>\epsilon > 0</math>, such that anything which will only happen with probability less than <math>\epsilon</math> is deemed ''impossible'' (IN THAT CONTEXT). There's an objection that it's "possible" to flip...") Tag: Visual edit
• 00:09, 23 April 2024 Lfox talk contribs created page Velocity (Created page with "The '''velocity''' of an object is the rate at which it moves. A particle is an entity considered as a point. == Specification == There is no such thing as the velocity of a particle at "an instant in time." But I want to specify a certain ''real'' measurement, which could actually be done, and which is the reality-based analogue of that notion. If one measures a particle and it is not moving (relative to me), then he can measure it at a certain position <math>x</m...") Tag: Visual edit
• 22:37, 22 April 2024 Lfox talk contribs created page Continuous (Redirected page to Continuity) Tags: New redirect Visual edit: Switched
• 20:13, 18 April 2024 Lfox talk contribs created page Real number (Created page with "I am not yet sure how to define real numbers. Many irrational numbers (e.g. <math>\sqrt{2}</math> and <math>\pi</math>) are in fact real, but the standard definition of the reals involves infinite nonsense. == Examples == Any fraction. Any algebraic number like <math>\sqrt{2}</math>. Pi e The output of the following computer program <code>digit(int i): if</code> <pre> digit(int i): if (suthaweou) return 0 </pre>") Tag: Visual edit: Switched
• 16:59, 18 April 2024 Lfox talk contribs created page Symmetry (Created page with "A '''symmetry''' is a change in perspective that renders a system unchanged. == Examples == [TODO picture] Imagine a square S with different sides (labels on each of its sides). You can rotate it, and you get a different square S'. But if you forget about the labels (omit the measurements of the labels), then S and S' are the same. This thing has a natural Z4 symmetry.") Tag: Visual edit
• 19:34, 10 April 2024 Lfox talk contribs created page Polynomial (Created page with "A '''polynomial''' is any function which obtains its result solely by some combination of: multiplying its inputs together, adding them together, or rescaling them. == Examples == The volume of a cube is a polynomial in its side length. Every linear transformation is uniquely associated to a polynomial called its characteristic polynomial. A computer program consisting of some number of <code>for</code> loops (and no recursion or <code>goto</code>...") Tag: Visual edit
• 05:18, 6 March 2024 Lfox talk contribs created page Information (Created page with "'''Information''' is a substance arranged in such a manner so as to convey knowledge to those who perceive it. [TODO is that right? It's consistent with saying "the words on this page are information" but not(?) with saying "the words on this page contain information." Information is not an irreducible primary, as some modern physicists think it is. Information presupposes the concepts of man and of knowledge. == Examples == Newspaper Brochure Wikipedia page Spe...") Tag: Visual edit
• 17:33, 14 February 2024 Lfox talk contribs created page Algorithm (Created page with "An '''algorithm''' is a sequence of simple tasks, steps, or operations that can be performed to compute values of a given function. == Examples == Schoolchildren learn algorithms for computing the sums, products, and ratios of numbers. There are algorithms to find the matrix resulting from the composition of two matrices. There can be no algorithm to compute whether two presentations generate the same group. == Time complexity == The time complexity of an alg...") Tag: Visual edit
• 04:12, 14 February 2024 Lfox talk contribs created page Coordinates (Created page with "A '''coordinate system''' is a system assigning a number (or tuple of numbers) to every point on an entity. The number (or tuple of numbers) assigned to a point is called the '''coordinate''' (or '''coordinates''') of the point. == Examples == Longitude and latitude are a coordinate system for the surface of the earth. If one picks two lines on a plane which meet at right angles, then one has implicitly chosen a Cartesian coordinate...") Tag: Visual edit
• 04:09, 14 February 2024 Lfox talk contribs created page Plane (Redirected page to Surface#Plane) Tags: New redirect Visual edit: Switched
• 02:51, 11 February 2024 Lfox talk contribs created page Existent (Created page with "An '''existent''' is an irreducible primary, and thus can only be defined ostensively. A circular definition of existent, which will help indicate what I'm talking about, is that it is "something that exists, be it a thing, an attribute or an action."<ref>Rand, Ayn. ''Introduction to Objectivist Epistemology''. Penguin, 1990.</ref> == Examples == Look at something around you. That is an existent. Consider one of its properties, like its shape or location or color. Tha...") Tag: Visual edit
• 19:41, 9 February 2024 Lfox talk contribs created page Zeno's Paradox (Created page with "'''Zeno's Paradox''' refers to<ref group="note">I call this Zeno's Paradox, but it is only loosely related to the historical Zeno. That is, I have made no attempt to conform to what Zeno himself actually said, or to understand what Zeno himself actually meant. Such historical questions are interesting, but not very relevant to Objective Mathematics.</ref> the following puzzle. To move any distance, one must first reach half the distance. After that, to close the remainin...") Tag: Visual edit: Switched
• 23:13, 2 February 2024 Lfox talk contribs created page Order (Created page with "A set <math>S</math> is said to possess an '''order''' (or, if necessary to disambiguate, a ''total'' order) if, for every pair of distinct elements <math>x,y \in S</math>, either <math>x</math> is ''before'' <math>y</math>, or <math>x</math> is ''after'' <math>y</math>, with respect to some order relation. Besides what Objective Mathematics means by "order," there are two other significant uses of the word. One refers to a command (an order) given to other people, as i...") Tag: Visual edit
• 04:18, 2 February 2024 Lfox talk contribs created page Nothing (Redirected page to Sets#The empty set) Tags: New redirect Visual edit: Switched
• 21:49, 30 January 2024 Lfox talk contribs created page Logicism (Redirected page to Formalism#Logicism) Tags: New redirect Visual edit: Switched
• 23:35, 27 January 2024 Lfox talk contribs created page Fraction (Created page with "A '''fraction''' is a concept which measures magnitude. == Rational numbers == Rational numbers, which we denote <math>\mathbb{Q}</math>, is concept of signed differences between fractions.") Tag: Visual edit
• 20:13, 26 January 2024 Lfox talk contribs created page Derivative (Created page with "Let <math>f : \mathbb{Q} \rightarrow \mathbb{Q}</math>, and let <math>\epsilon : \mathbb{Q}</math> be positive. We define <math>\Delta_\epsilon f : \mathbb{Q} \rightarrow \mathbb{Q}</math> by<math display="block">(\Delta_\epsilon f) (x) := \frac{f(x + \epsilon) - f(x)}{\epsilon}. </math>We say that <math>f</math> is '''differentiable''' if is .... nill whenever") Tag: Visual edit
• 20:07, 26 January 2024 Lfox talk contribs created page Differentiable (Redirected page to Derivative) Tags: New redirect Visual edit: Switched
• 22:28, 25 January 2024 Lfox talk contribs deleted page File:Cat mouse 2.jpg (content was: "== Summary == a picture of a cat", and the only contributor was "Lfox" (talk))
• 23:05, 24 January 2024 Lfox talk contribs created page Category:Irreducible primaries (Created page with "Similar to the categories Aristotle gave * Entity * Before, after * Existent * Set * Attribute * Relation * Quantity") Tag: Visual edit
• 08:41, 24 January 2024 Lfox talk contribs created page Ordering (Created page with "I don't really know what an '''ordering''' is. It has something to do with order and disorder, but I'm not clear on exactly what the relation is. It is also an interesting fact that the verb "to order" means both ''to give a command'', and ''to endow with order; to make something fit a certain pattern''. I doubt that this is a coincidence. Like, to order some books is to impose your will on them, by making them fit a certain pattern. == Examples == Library books are...") Tag: Visual edit
• 06:18, 24 January 2024 Lfox talk contribs created page Quantities (Redirected page to Quantity) Tag: New redirect
• 06:18, 24 January 2024 Lfox talk contribs created page Numbers (Redirected page to Quantity) Tag: New redirect
• 06:18, 24 January 2024 Lfox talk contribs created page Number (Redirected page to Quantity) Tag: New redirect
• 22:50, 23 January 2024 Lfox talk contribs created page Formalism (Created page with "'''Formalism''' is a philosophy of mathematics, which holds that math is just a game of formal symbol manipulation, and that mathematical objects ''per se'' don't exist at all. Formalism has the same flavor as subjectivism. Many formalists are only formalists with respect to some parts of math. This includes most working mathematicians, insofar as they hold formalist premises. For example, Hilbert held<ref>Brown, James R. ''Philosophy of Mathematics: An Introduction...") Tag: Visual edit
• 21:29, 23 January 2024 Lfox talk contribs created page Intuitionism (Created page with "'''Intuitionism''' is a philosophy of mathematics, which holds that mathematical objects exist in intuition. Intuitionism is based, fairly directly, on the philosophy of Immanuel Kant. == Examples == Bold mine. From Jacob Lurie, ''Higher Topos Theory''<ref>Lurie, Jacob. ''Higher Topos Theory''. Princeton, N.J., Princeton University Press, 2009.</ref>:<blockquote>Unfortunately, not every <math>\infty</math>-topos <math>\mathcal{X}</math> can be obtained as topol...") Tag: Visual edit
• 00:09, 22 January 2024 Lfox talk contribs created page Points (Redirected page to Point) Tags: New redirect Visual edit: Switched
• 19:10, 21 January 2024 Lfox talk contribs created page Platonism (Created page with "'''Platonism''' is a philosophy of mathematics which holds that mathematical concepts are real Platonism is one of the three philosophies which dominate modern mathematics, the others being Intuitionism and Formalism/Logicism. However, few if any mathematicians adhere consistently to any of those three philosophies. Platonism dates back to Plato and Socrates. The term "Platonism" is also sometimes used to refer to the philosophy of Plato generally.") Tag: Visual edit
• 05:36, 21 January 2024 Lfox talk contribs created page Line (Created page with "A '''line''' is a straight curve. Straightness is recognized perceptually. Lines are one of the central concepts of classical geometry. Unlike standard mathematics, the concept of a line in Objective Mathematics refers to real things, and real things have finite thicknesses and are never completely straight.") Tag: Visual edit
• 05:25, 21 January 2024 Lfox talk contribs created page Entity (Created page with "An '''entity''' is an irreducible primary, and can therefore only be defined ostensively. To get a better idea, <blockquote>This term [entity] may be used in several senses. If you speak in the primary sense, “entity” has to be defined ostensively—that is to say, by pointing. I can, however, give you three descriptive characteristics essential to the primary, philosophic use of the term, according to Objectivism. This is not a definition, because I’d have to rel...")
• 05:18, 21 January 2024 Lfox talk contribs created page File:Airbus A380.jpg (an airplane)
• 05:18, 21 January 2024 Lfox talk contribs uploaded File:Airbus A380.jpg (an airplane)
• 05:15, 21 January 2024 Lfox talk contribs created page File:Saturn on June 29, 2016 (31437313530).jpg (the planet Saturn)
• 05:15, 21 January 2024 Lfox talk contribs uploaded File:Saturn on June 29, 2016 (31437313530).jpg (the planet Saturn)
• 05:14, 21 January 2024 Lfox talk contribs created page File:Hot dog with mustard.png (a hot dog with mustard)
• 05:14, 21 January 2024 Lfox talk contribs uploaded File:Hot dog with mustard.png (a hot dog with mustard)
• 05:10, 21 January 2024 Lfox talk contribs created page File:Brick.jpg (a brick)
• 05:10, 21 January 2024 Lfox talk contribs uploaded File:Brick.jpg (a brick)
• 05:09, 21 January 2024 Lfox talk contribs created page File:Cat outside.jpg (a picture of a cat)
• 05:09, 21 January 2024 Lfox talk contribs uploaded File:Cat outside.jpg (a picture of a cat)
• 05:08, 21 January 2024 Lfox talk contribs created page File:Cat mouse 2.jpg (a picture of a cat)
• 05:08, 21 January 2024 Lfox talk contribs uploaded File:Cat mouse 2.jpg (a picture of a cat)