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Prove that a finite cartesian product of countable sets is countable?
Wiki User
∙ 15y ago
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
Wiki User
∙ 15y ago
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How does transformations prove that two triangles are similar?
By enlargement on the Cartesian plane and that their 3 interior angles will remain the same
How do you prove that a finite set of points cannot have any accumulation points in a real analysis?
If you have a finite set of points (call them A1, A2, A3...), then you have a finite set of distances to the points. So for any point B, simply pick a distance D that's smaller than the distance between B and A1, the distance between B and A2, and so on. (This is possible, since there a finite number of points.) ================================================ Since there are no points within distance D of B (because this is how you chose D), point B can not be an accumulation point (because an accumulation point must have points within any given distance of it)
How do you use inductive reasoning to prove the product of an odd integer and an even integer will always be even?
The product of an odd and even number will always have 2 as a factor. Therefore, it will always be even.
How do you prove that the product of two consecutive even integers is divisible by 8?
Because 6*8 = 48 and 48/8 = 6
What is the connection between Euclid and prime numbers?
Euclid (c. 300 BC) was one of the first to prove that there are infinitely many prime numbers. His proof was essentially to assume that there were a finite number of prime numbers, and arrive at a contradiction. Thus, there must be infinitely many prime numbers. Specifically, he supposed that if there were a finite number of prime numbers, then if one were to multiply all those prime numbers together and add 1, it would result in a number that was not divisible by any of the (finite number of) prime numbers, thus would itself be a prime number larger than the largest prime number in the assumed list - a contradiction.
Prove that countable space is countable?
prove that every metric space is hausdorff and first countable
Is every subset of a finite set is a finite?
prove that every subset of a finite set is a finite set?
How does transformations prove that two triangles are similar?
By enlargement on the Cartesian plane and that their 3 interior angles will remain the same
How prove that the set of irrational numbers are uncountable?
Proof By Contradiction:Claim: R\Q = Set of irrationals is countable.Then R = Q union (R\Q)Since Q is countable, and R\Q is countable (by claim), R is countable because the union of countable sets is countable.But this is a contradiction since R is uncountable (Cantor's Diagonal Argument).Thus, R\Q is uncountable.
Every permutation can be written as a product of transposition. How to prove or just apparently?
Prove it using deduction._______First you prove, that every permutation is a product of non-intercepting cycles, which are a prduct of transpsitions
What evidence do you need to prove that i exist?
Try the Cartesian Method: if you think you exist (or even if you doubt you exist) then clearly something is doing that thinking; that something is you.
What are the limitations of finite automata?
The defining characteristic of FA is that they have only a finite number of states. Hence, a finite automata can only "count" (that is, maintain a counter, where different states correspond to different values of the counter) a finite number of input scenarios.There is no finite automaton that recognizes these strings:The set of binary strings consisting of an equal number of 1's and 0'sThe set of strings over '(' and ')' that have "balanced" parenthesesThe 'pumping lemma' can be used to prove that no such FA exists for these examples.
How do you prove that order of a group G is finite only if G is finite and vice versa?
(1). G is is finite implies o(G) is finite.Let G be a finite group of order n and let e be the identity element in G. Then the elements of G may be written as e, g1, g2, ... gn-1. We prove that the order of each element is finite, thereby proving that G is finite implies that each element in G has finite order. Let gkbe an element in G which does not have a finite order. Since (gk)r is in G for each value of r = 0, 1, 2, ... then we conclude that we may find p, q positive integers such that (gk)p = (gk)q . Without loss of generality we may assume that p> q. Hence(gk)p-q = e. Thus p - q is the order of gk in G and is finite.(2). o(G) is finite implies G is finite.This follows from the definition of order of a group, that is, the order of a group is the number of members which the underlying set contains. In defining the order we are hence assuming that G is finite. Otherwise we cannot speak about quantity.Hope that this helps.
What historical antecedent to consumer protection occurred in the 1950s?
a significant breakthrough occurred with the establishment of the product-liability concept, whereby a plaintiff did not have to prove negligence but only had to prove that a defective product caused an injury
How does lemon can be use in feasibility study?
what are you trying to prove? if you were trying to prove a lemon can make lemonade the lemon can be used as a product to ensure that the theory is in fact "feasible"
Prove that 77777 is a staircase composite?
It is a stair case composite as it is the product of 7, 41, and 271.
Do Prove that the product of an integer and arbitrary integer is even?
The statement is not true. Disprove by counter-example: 3 is an integer and 5 is an integer, their product is 15 which is odd.
