1. P

    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. B

    I can't understand how to prove limits using the definition...

    \lim_{x \to c} f(x) = L if \forall ε > 0, \exists δ>0 : 0 < |x-c| < δ => |f(x) - L| < ε , \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. M

    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. B

    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. C

    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. D

    Is the Is definition of a ‘point’ in geometry contradictory?

    “A 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 attribute” If a point has no length it does not exist so...
  7. S

    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. L

    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. B

    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. M

    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 ϵ>0...
  11. Z

    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:
  12. N

    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. D

    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. R

    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. L

    on Vertical line test and definition of a function

    Vertical line test “A function can only have one output, y, for each unique input, x.” – from Wikipedia Why do we want a function to have only one output?
  16. E

    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. H

    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: _________________________________________________________________...
  18. N

    find the definition area of the function

  19. L

    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. M

    conics definition

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