what's "factal"?It's a mathematical expretion (I think)?
143020
the word is "fractal". Go look it up.
710728
A lot of places offer "Analysis," which comes after Calculus. I think it largely deals with proving things in math... like actually proving the things in Calculus that we learned were true.
912026
For everyday general physics we can rely fully on maths.as basic problems solved are already established by experiments.for example in general gravitation,electrostatics,magnetics.maths used in these areas is also confirmed by a great extent to s.\n \nBUT we don't establish a physical fact by mathematical calculation only.it is established only after theoretical proof.for ex till date we call theory of relativity only "THEORY" while it is established by both logical and mathematical proofs.there are some experimental evidences also but they are not strong enough to establish this theory beyond question.\n     \n \nso basically physics don't rely on math but math is used only as a tool for our logical findings of physics whenever and wherever required.
749336
What is the interesting fact?!@
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I can't help you justify generalizations, however, I can type about use of it in logic.  \n\nFallacies:\n\n1.)  Accident:  When one applies a generalization to an individual case that it does not properly govern. \n\n2.)  Converse Accident:   When one moves carelessly or too quickly from a single case to an indefensibly broad generalizaiton.\n\nAssumptions:\n\n1.)  An assumption is an induction.  Its like assuming the sun will rise tomorrow.  We assume its going to happen because it has for millions of years.   \n\n2.) The bad thing about assumption is that you are using probabilities to create a conclusion.
1010373
Newton advanced it as an axiom, by virtue of which it wouldn't be "proven", only tested (the resulting predictions tested.) If I say "suppose I assume a space where all parallel lines converge", I don't "prove" my assumption - it's an assumption. You work outward from it and see what you get. If what you get is impossible (or wrong), it was a bad assumption.
259386
http://en.wikipedia.org/wiki/Logical_fallacy
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So X is dependent on TSOUT (the source of universal truth)\n\nAnd the TSOUT is dependent on X.\n\nThat, my friend, is circular logic, and as such, is a false proof.
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Obvious\n\nWordNet (r) 2.0 [wn]\nself-evident\n     adj : evident without proof or argument; "an axiomatic truth"; "we\n           hold these truths to be self-evident" [syn: axiomatic,\n            taken for granted(p)]\n\nEvident &#92;Ev"i*dent&#92;, a. [F. ['e]vinent, l. evidens, -entis; e\n   out + videns, p. pr. of videre to see. See Vision.]\n   Clear to the vision; especially, clear to the understanding,\n   and satisfactory to the judgment; as, the figure or color of\n   a body is evident to the senses; the guilt of an offender can\n   not always be made evident.\n   [1913 Webster]
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When I call something a fact it is not really a fact but rather an assumed fact.\n\nFact: God is defined as being greater than anything that can be imagined. ( The defined as is an important part of the proof)\n\nFact: God exists in understanding. (a person can imagine that a god exists)\n\nFact(dubious): If God exists in understanding, We can imagine him as greater if he exists in reality. ( The idea is if you imagine the great god as only existing in our imagination, and then imagine him existing in reality He would be greater in the case where he exists in reality.)\n\nNow here is the squeeze play. Go back to the definition of god as being greater than anything that can be imagined. Now of the two possibilities, that god exists only in our imagination, and God exists in reality, only the later that god exists in reality fits the definition of God, Therefore according to this logical construct God Must exists. I like to call this a logic box. You build parameter that insures an outcome that God exists. \n\nThe problem shows up in that are all the facts real, and also just because something can be logically shown to fit a definition is the definition true.
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Working backwards from your conclusion, but following your logic, you have not joined 2 ones with 2 ones, but rather joined 2 tens with 2 ones.  However you have used the same symbol to represent both the 2 tens and the 2 ones, which is the flaw in your logic.\n\nIn mathematics means adding, not merely joining together, and the column placement of the inputs and the results cannot be disregarded.
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You are thinking of the book 'Principia Mathematica' by (Bertrand) Russell and Whitehead, written in 1913. The book was actually dedicated to putting mathematics on a logical foundation. It uses rather antiquated notation and really didn't accomplish what it intended to do, but it was a massive effort. The statement that 1+1=2 came in the middle of the second volume of the three volume set. There is a paperback version for about the first half of the first volume that is still available.
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Extrapolation is a process of logical induction.  You take a trend from observations, and assume a trend holds in order to predict the outcome of a hypothetical observation.
146626
What exactly is that?
600176
This is a Frequently Asked Question. Following is my previous answer:\n\nThis hypothesis is false:\nSuppose 0/0 = 1. Since 1 is the multiplicative identity, this implies (0/0)*a = a for all real numbers a. But (0/0)*a = (0*a)/0 = 0/0 = 1. This contradicts our hypothesis that 0/0 is the multiplicative identity, so the hypothesis must be false (proof by contradiction). QED\n0/0 is indeterminate as a limiting form. See http://mathworld.wolfram.com/Indeterminate.html .\nAs an algebraic expression over the real field, it is undefined: http://mathworld.wolfram.com/Undefined.html .\nThis is a Frequently Asked Question; the following is my previous answer:\n\nThis question may be asked so frequently (along with the infamous 0.999...) because no concrete axioms or definitions are ever given for the real number system until one studies higher algebra or real analysis; it is assumed that everyone knows what a real number is until then. The proliferation of these questions show that this assumption is no good.\nFor the sake of conciseness, I will not define what a real number is here, as only the algebraic structure of the real numbers is necessary to answer this question. The algebraic structure of the real numbers is what we call a field. A field is an algebraic structure that follows a finite set of axioms. These axioms define what statements are true and false in this system based on the laws of logic. You can find the field axioms here: http://mathworld.wolfram.com/Field.html .\nEach line is preceded by "For all real numbers a, b and c, the following is true...". Note that the proper form of the additive identity and multiplicative identity is that it prescribes the existence of some number 1 and some number 0 such that the equations hold. These same numbers are then used to prescribe the existence of additive and multiplicative inverses.\nDivision a/b is just shorthand for a*(b^(-1)). So in your question, you are looking for 0*0^(-1). It is easy to show that there is no such number as 0^(-1) in any field. Suppose 0^(-1) exists.\nThen 0*0^(-1) = 1. But multiplying both sides by 0^(-1) gives 0 = 0^(-1), which means 0*0 = 0 = 1. This is obviously false.\nSuppose 0 = 1. 0*a = a for all numbers a. But 0*a = (1 + (-1))*a = a + (-a) = 0. Thus 0 is not equivalent to 1 and our sole assumption that 0^(-1) exists must be false. Thus the expression 0*0^(-1) is undefined in a field.\nProof by contradiction is very powerful for many types of statements.\nAs for trying to define 0/0 using limiting behavior, note that you are evaluating a limit over a plane of the function f(x,y) = x/y. As we approach (0,0) along the x-axis, this limit is 0, but as we approach (0,0) along the y-axis, the limit diverges. Thus, the limit of f(x,y) at (0,0) does not exist, so f(0,0) remains undefined with no continuous way to complete it. The limit is not indeterminate for this function; it does not exist.\nThe expression 0/0 is said to be indeterminate as a limiting form because one can have many functions that approach the form 0/0 that have convergent limits of different values. For example, the limit as x approaches 0 of [sin(x)]/x yields the indeterminate form 0/0, but L'Hopital's rule reveals the limit to be 1. Similarly, multiplying the above limiting form by any real number will yield that number as the limit, even though the form is still 0/0. The expressions listed on this page: http://mathworld.wolfram.com/Indeterminate.html are called indeterminate because they do not have a fixed behavior when studied as limits of expressions.
800839
Mathematics is the language of science.  It is how scientific models are defined and universally understood.
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You don't understand the definition of a theory and a fact do you? I presume, judging from your words, you believe that a theory is essentially a conjecture, a guess, that sort of thing? Well, you thought wrong.\n\nScientific definitions and mathematical definitions are far different and more precise than everyday language. For us, a salt is that white stuff that preserves foods and gives the food, obviously enough, that "salty" taste. In chemistry, a salt is any ionic compound formed by anions and cations so that the net charge of the compound is neutral. \n\nIn that same manner, a theory is not just a "guess." Theories and facts are not rungs on a ladder of credibility - they complement each other. Theories are really models for explaining a series of natural phenomena, backed by strong evidence. Theories explain facts. Again, they are not "guesses."\n\nAnd, in that manner, evolution is both a theory AND a fact. There is the theory of evolution, which explains it, and there is the fact of evolution. This is similar to the theory of gravity; how the theory explains the fact that gravity exist, and the reason why apples fall down and hit us on the head. \n\nThere is plenty of evidence to support evolution and it is a strongly-backed theory. Also, all theories are incomplete and subject to revision. That applies to all theories - not just evolution. The atomic theory expanded over the last century as the Bohr model evolved into the current electron-cloud model. \n\nAlso, another misconception to clear up - there is nothing proven in science; there is just evidence to support it.\n\nAlso, people who criticize evolution often forget that it doesn't deal with the origin of life, it is NOT random, that the concept of uniformitarianism in science make evolution valid, etc.\n\nI suggest you read a little.