# definition

1. ### Definition and sets

The following sentence, a set is infinite if and only if the set have a bijection with itself, the negation of the affirmation is true? A set is finite if only if there doesn't exist any bijection with itself? The idea is what is a better definition of a bijection in this case. (Sorry, guys...
2. ### I can't understand how to prove limits using the definition...

\lim_{x \to c} f(x) = L if \forall Îµ > 0, \exists Î´>0 : 0 < |x-c| < Î´ => |f(x) - L| < Îµ , \forall x maybe except c. First of all do I understand what the definitions says? My understanding is this: "The closer x is at c the more precisely f(x) will approach L." In order to define this...
3. ### Definition of Formal power series in m indeterminates over R

I could not understrand the following definition for formal power series over $m$ indeterminates, over the commutative ring $R$: *I do understand:* We set $R[\![X_{1},...,X_{m}]\!]:=(R^{(\mathbb{N}^{m})},+,.)$, where $+$ and $.$ are as in: $(p+q)_{\alpha}:=p_{\alpha}+q_{\alpha}$...
4. ### Definition of the angle and pi???

As a University student, I'm re-reading calculus in order to get a full understanding of what is going on and how everything was actually invented (I just love to know how things work). By reading calculus 1 of Thomas and Finney I found out for the first time that the angle in radians is...
5. ### Recursive definition and induction

Hey. The series $a_n$ is defined by a recursive formula $a_n = a_{n-1} + a_{n-3}$ and its base case is $a_1 = 1 \ a_2 = 2 \ a_3 = 3$. Prove that every natural number can be written as a sum (of one or more) of different elements of the series $a_n$. Now, I know that is correct intuitively...
6. ### Is the Is definition of a â€˜pointâ€™ in geometry contradictory?

â€œA point is defined only by some properties, called axioms, that it must satisfy. In particular, the geometric points do not have any length, area, volume or any other dimensional attributeâ€ https://en.m.wikipedia.org/wiki/Point_(geometry) If a point has no length it does not exist so...
7. ### A new definition for a superset of Carmichael numbers

We define a so-called Extended Korselt Pseudoprime in the following way: A composite number N is an Extended Korselt Pseudoprime iff for all prime divisors F of (N-1) the congruence F^(N-1) = 1 mod N holds true. Incidentally the theorem does have at least one practical application: the Lucas...
8. ### Newton's method vs. limit definition

Can Newton's method be effective in defining limits with an epsilon-delta form? Or, is it relatively intractable for intricate, yet linear curves upon approaching the infinitesimal level -- more than the traditional definition?
9. ### Rational equation definition

Hi everyone, Stuck with this definition question. What is the meaning of a rational equation A) Two rational expressions having equal domains. B) The set of X values which satisfy two rational expressions. C) Two rational expressions which are equal to each other. D) Any equation having...
10. ### Showing a sequence does not diverge to infinity using definition

Is there a definition for a sequence that does not diverge to infinity? Can I negate the definition of divergence to infinity of sequence, like I can do with convergence? What I mean is, convergent sequence definition is: "A sequence (an) is said to converge to L provided that for each Ïµ>0...
11. ### A Definition of Topology

"Basic concept (building blocks) of Topology: A set and all it's subsets. "X" Topology: A Set and a specific collection of subsets known as "open subsets." (S,s). If "open subsets" = open subsets, you have Euclidean Topology. REF: http://mymathforum.com/topology/341533-neighbourhood-point-6.html
12. ### Use the definition of the integral as a limit of a Riemann sum

Equation: "integral from 0 to 6 of -(x^2)+36" I know how to find it the easy way... Ex.) I know to take the integral -(x^3)/3+36x and evaluate it from 0 to 6 which = (-216/3) + 216 == [144] So I know the answer, I just don't understand what my teacher wants. I know there's an...
13. ### Definition of a random variable

Hi guys Definition from book: A random variable $X$ is defined to be a numerically valued function of the elementary events $Ei$ what does it mean it plain english? I understand the numerical and the random aspect but how is it a function of events?
14. ### Definition of Division

Help me out with this intuition. (124 + 104 + 84 + 64 + 44 + 24) / (62 + 52 + 42 + 32 + 22 + 12) Why is the answer 2 and not 12. If division is multiplication of the reciprocal and we pair a number from the left with one from the right that should get us 2 + 2 + 2 +2 +2 +2 ? 124 X...
15. ### on Vertical line test and definition of a function

Vertical line test â€œA function can only have one output, y, for each unique input, x.â€ â€“ from Wikipedia Why do we want a function to have only one output?
16. ### Difference between parabola & hyperbola --simple definition

Hi --- As a complete math idiot ( failed high school math twice ) but achieved above average results in all other subjects -- Persistent problem ---a rifle trajectory ---is shown as a parabola --PARABOLA ? I d/loaded a parabola --- X= Y squared-----images ---etc quite simple ---a...
17. ### Rigorous definition of "Differential"

First of all I want to clarify that I posted this question on many forums and Q&A websites so the chances of getting an answer will be increased. So don't be surprised if you saw my post somewhere else. Now let's get started: _________________________________________________________________...

19. ### Is dark matter sans E-M by definition?

Has it been shown that dark matter candidates do not emit light at any wavelength? How about Hawking radiation by black holes, or decay of the Higgs boson?
20. ### conics definition

Hello, What is definition of conic is it a branch of math or a topic?