Let (mathscr{F}:={F subset mathbb{N}: # F
Question:
Let \(\mathscr{F}:=\{F \subset \mathbb{N}: \# F<\infty\}\). Show that \(\# \mathscr{F}=\# \mathbb{N}\).
[ embed \(\mathscr{F}\) into \(\bigcup_{k \in \mathbb{N}} \mathbb{N}^{k}\) or show that \(F \mapsto \sum_{j \in F} 2^{j}\) is a bijection between \(\mathscr{F}\) and \(\mathbb{N}\).]
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (2 reviews)
Data from theorem 27 Let FF with F n The...View the full answer
Answered By
Susan Juma
I'm available and reachable 24/7. I have high experience in helping students with their assignments, proposals, and dissertations. Most importantly, I'm a professional accountant and I can handle all kinds of accounting and finance problems.
4.40+
15+ Reviews
45+ Question Solved
Related Book For
Question Posted:
Students also viewed these Business questions
-
Let H be a nonempty, closed, bounded subset of Rn. a) Suppose that f : H Rm is continuous. Prove that is finite and there exists an x0 H such that ||f(x0)|| = ||f||H. b) A sequence of functions fk: H...
-
7. The ball is thrown from point A with a velocity of 50 m/s at the angle shown. a) Determine the velocity at t = 2 second. (10%) b) Determine the radius of curvature at t = 2second. (15%) 130 "(.
-
Let E be a nonempty subset of R and f be a real-valued function defined on E. Suppose that fn is a sequence of bounded functions on E which converges to f uniformly on E. Prove that uniformly on E as...
-
You have been asked, as a consultant, by the chief compliance officer of a multi-facility health system to assist in evaluating the organizations current enterprise-wide coding compliance plan for...
-
An electric resistance heater is embedded in a long cylinder of diameter 30 mm. When water with a temperature of 25C and velocity of 1 m/s flows crosswise over the cylinder, the power per unit length...
-
As part of its initiative to implement just-in-time (JIT) manufacturing at the motorcycle assembly plant in Exercise 1, Harley has reduced the number of engines loaded on each truck to 100. If each...
-
What is a writ of execution?
-
National Tennis Racquet Co. produces and sells three models: Required (Round all percentages to 2 decimal places and monetary calculations to the nearest dollar.) a. What is the weighted average...
-
Blake was 21 years of age at the end of the year. During the year, he was a full-time college student. He also worked part-time and earned $8,000, which he used to pay all $6,000 of his living...
-
Show - not using Theorem 2.10 - that \(\# \mathscr{P}(\mathbb{N})>\# \mathbb{N}\). Conclude that there are more than countably many maps \(f: \mathbb{N} ightarrow \mathbb{N}\). [ use the diagonal...
-
Show that if \(E \subset F\) we have \(\# E \leqslant \# F\). In particular, subsets of countable sets are again countable.
-
Barry, Hank, and Babe form a company named Long Ball Investments, hoping to find that elusive home run stock. A new clothing company by the name of Major League Apparel has caught their eye. Major...
-
Simplify: xx.x13
-
Could you please provide the yield to maturity for a 21-year bond with a coupon rate of 7.76 percent per annum, a par value of $1,000, and a current price of $946? Please ensure that the answers are...
-
A married couple with 3 children is filing taxes jointly. They have a gross income of $ 5 2 , 3 2 2 , and they made the following tax - deductible purchases: Charitable contributions: $ 5 , 9 1 5...
-
2-Discuss the benefits and potential challenges of recognizing religious diversity in the workplace .
-
The following accounts are in Whispering Winds Limiteds December 3 1 , 2 0 2 3 trial balance: Prepaid Rent $ 1 , 5 0 0 ; FV - OCI Investments $ 6 9 , 0 0 0 ; Unearned Revenue $ 8 , 1 0 0 ; Land Held...
-
Use the following facts of Lilac Corporation to prepare its journal entries relating to the (a) Manufacturing of inventory, (b) Revenue recognition during production, (c) Partial billing, (d) Cash...
-
Suppose the concentration of glucose inside a cell is 0.1 mm and the cell is suspended in a glucose solution of 0.01 mm. a. What would be the free energy change involved in transporting 10-o mole of...
-
A taxpayer sells a warehouse for a recognized gain. Depreciation had been properly claimed on the property, based on the straight-line method over a 39-year recovery period. Will the same amount of...
-
Osprey Corporation, a closely held corporation, has $100,000 of net active income, $25,000 of portfolio income, and a $120,000 loss from a passive activity. a. How much of the passive loss can Osprey...
-
Marmot Corporation pays a dividend of $100,000 in the current year. Otter Corporation, which is in the 25% marginal bracket, owns 15% of Marmots stock. Gerald, an individual taxpayer in the 25%...
-
3-17. Solve the following differential equations by means of the Laplace transform. d f(t) (a) dt [dx(t) df (t) dt +5- +4(t)=eu(t) (Assume zero initial conditions.) = x(t) =2x(t)3x2(t)+us(t)x,...
-
Rent expense in Marin Company's Year 2 income statement is $305,000. If Prepaid Rent was $48,000 at December 31, Year 1, and is $100,000 at December 31, Year 2, the cash paid for rent during Year 2...
-
Pringle Manufacturers had an inventory of 10 000 units of Product B at a production cost of R11 per unit on 01 January 2024. An additional 60 000 units are expected to be produced during 2024. The...
Study smarter with the SolutionInn App