A Activity diagram used in UML 6/9 and SysML B Bachman diagram Booch used in software engineering Block diagram Block Definition Diagram BDD used in SysML C Carroll diagram Cartogram Catalytic cycle Chemical equation Curly arrow diagram Category theory diagrams Cause-and-effect diagram Chord diagram Circuit diagram Class diagram from UML 1/9 Collaboration diagram from UML 2.0 Communication diagram from UML 2.0 Commutative diagram Comparison diagram Component diagram from UML 3/9 Composite structure diagram from UML 2.0 Concept map Constellation diagram Context diagram Control flow diagram Contour diagram Cordier diagram Cross functional flowchart D Data model diagram Data flow diagram Data structure diagram Dendrogram Dependency diagram Deployment diagram from UML 9/9 Dot and cross diagram Double bubble map used in education Drakon-chart E Entity-Relationship diagram ERD Event-driven process chain Euler diagram Eye diagram a diagram of a received telecommunications signal Express-G Extended Functional Flow Block Diagram EFFBD F Family tree Feynman diagram Flow chart Flow process chart Flow diagram Fusion diagram Free body diagram G Gantt chart shows the timing of tasks or activities used in project management Grotrian diagram Goodman diagram shows the fatigue data example: for a wind turbine blades H Hasse diagram HIPO diagram I Internal Block Diagram IBD used in SysML IDEF0 IDEF1 entity relations Interaction overview diagram from UML Ishikawa diagram J Jackson diagram K Karnaugh map Kinematic diagram L Ladder diagram Line of balance Link grammar diagram M Martin ERD Message Sequence Chart Mind map used for learning, brainstorming, memory, visual thinking and problem solving Minkowski spacetime diagram Molecular orbital diagram N N2 Nassi Shneiderman diagram or structogram a representation for structured programming Nomogram Network diagram O Object diagram from UML 2/9 Organigram Onion diagram also known as "stacked Venn diagram" P Package diagram from UML 4/9 and SysML Parametric diagram from SysML PERT Petri net shows the structure of a distributed system as a directed bipartite graph with annotations Phylogenetic tree - represents a phylogeny evolutionary relationships among groups of organisms Piping and instrumentation diagram P&ID Phase diagram used to present solid/liquid/gas information Plant Diagram Pressure volume diagram used to analyse engines Pourbaix diagram Process flow diagram or PFD used in chemical engineering Program structure diagram R Radar chart Radial Diagram Requirement Diagram Used in SysML Rich Picture R-diagram Routing diagram S Sankey diagram represents material, energy or cost flows with quantity proportional arrows in a process network. Sentence diagram represents the grammatical structure of a natural language sentence. Sequence diagram from UML 8/9 and SysML SDL/GR diagram Specification and Description Language. SDL is a formal language used in computer science. Smith chart Spider chart Spray diagram SSADM Structured Systems Analysis and Design Methodology used in software engineering Star chart/Celestial sphere State diagram are used for state machines in software engineering from UML 7/9 Swim lane Syntax diagram used in software engineering to represent a context-free grammar Systems Biology Graphical Notation a graphical notation used in diagrams of biochemical and cellular processes studied in Systems biology System context diagram System structure Systematic layout planning T Timing Diagram: Digital Timing Diagram Timing Diagram: UML 2.0 TQM Diagram Treemap U UML diagram Unified Modeling Language used in software engineering Use case diagram from UML 5/9 and SysML V Value Stream Mapping Venn diagram Voronoi diagram W Warnier-Orr Williot diagram Y Yourdon-Coad see Edward Yourdon, used in software engineering
Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product of 0 and anything is 0 0, and seems like it would be reasonable to assume that 0! = 0 0! = 0. I'm perplexed as to why I have to account for this condition in my factorial function (Trying to learn Haskell ...
Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was considered i...
A value of "0" doesn't tell the reader that we actually do know that the value is < 0.1. Would we not want to report it as 0.00? And if so, why wouldn't we also say that it has 2 significant figures? In other words, saying something has zero significant figures seems to throw out valuable information. What is the downside of handling 0 as an ...
0i = 0 0 i = 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x = 0 0 x = 0. On the other hand, 0−1 = 0 0 1 = 0 is clearly false (well, almost —see the discussion on goblin's answer), and 00 = 0 0 0 = 0 is questionable, so this convention could be unwise when x x is not a positive real.
For example, 0x = 0 0 x = 0 and x0 = 1 x 0 = 1 for all positive x x, and 00 0 0 can't be consistent with both of these. Another way to see that 00 0 0 can't have a reasonable definition is to look at the graph of f(x, y) =xy f (x, y) = x y which is discontinuous around (0, 0) (0, 0). No chosen value for 00 0 0 will avoid this discontinuity.
The argument seems to hinge on whether one is to define 0^0=1 and economize several definitions and theorems from algebra, combinatorics, and analysis, at the expense of one caveat for a single function, OR to leave 0^0 undefined, have several caveats so as to preserve the continuity on the domain of definition of a single function, namely x^y.
0 0 = x 0 0 = x 0x = 0 0 x = 0 x x can be any value, therefore 0 0 0 0 can be any value, and is indeterminate. 1 0 = x 1 0 = x 0x = 1 0 x = 1 There is no such x x that satisfies the above, therefore 1 0 1 0 is undefined. Is this a reasonable or naive thought process? It seems too simple to be true.
93 The other comments are correct: 1 0 1 0 is undefined. Similarly, the limit of 1 x 1 x as x x approaches 0 0 is also undefined. However, if you take the limit of 1 x 1 x as x x approaches zero from the left or from the right, you get negative and positive infinity respectively.
A 0 0 form on a vector space is just a scalar. A 0 0 form on a manifold is a function (i.e. it assigns a scalar to each tangent space of the manifold).
5 We have x0:= 1 x 0:= 1 for every complex number x x. (Notice that this is the only convention which fits into the rules of arithmetic, and there is no need to exclude x = 0 x = 0. Think about the binomial theorem, for instance.) By the way, your exercise ∑1000 n=0 in ∑ n = 0 1000 i n can be solved with the usual formula for geometric series.
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