Question

In: Advanced Math

Please justify below questions (its a topology question) with valid arguments: 1. Show that an infinite...

Please justify below questions (its a topology question) with valid arguments:

1. Show that an infinite set is not finite.

2. Is there an infinite set which is not countably in finite?

Thanks in advance.

Solutions

Expert Solution


Related Solutions

X is infinite set with the finite complement topology. X is Hausdorff ??? why??? please thank...
X is infinite set with the finite complement topology. X is Hausdorff ??? why??? please thank U
a) Use truth tables to show that the following are valid arguments: i. [p  (p...
a) Use truth tables to show that the following are valid arguments: i. [p  (p → q)] → q ii. [(p → q) ∧ (q → r)] → (p → r) b) Use truth tables to show the logical equivalence of: i. (p → q) ⇔ (¬p ∨ q ) ii. (¬p ∨ q) ∨ (¬p  q) ⇔ p
Please answer the questions in the space provided below each question. Show all of your work...
Please answer the questions in the space provided below each question. Show all of your work and circle your final answer. You forecast there are three potential scenarios for the economy: a bull, flat, and bear market. You also estimate the returns for a stock and bond mutual fund as follows: Economic Scenario Stock Fund Bond Fund Probability of Scenario Recession -18% 6% 0.3 Flat 8% 4% 0.45 Boom 20% -8% 0.25 Using this information, you find for the stock...
Topology question: Show that a function f : ℝ → ℝ is continuous in the ε...
Topology question: Show that a function f : ℝ → ℝ is continuous in the ε − δ definition of continuity if and only if, for every x ∈ ℝ and every open set U containing f(x), there exists a neighborhood V of x such that f(V) ⊂ U.
Please use any of the methods to prove whether each of the following arguments is valid...
Please use any of the methods to prove whether each of the following arguments is valid or invalid. For each problem, please identify the method that you have decided to employ and make sure to show your work. 1. It is obvious that nuclear energy is needed. Nuclear energy is needed if and only if solar energy cannot be harnessed. And it is also true both that solar energy can be harnessed only if funds to do so are available,...
5. For each set below, say whether it is finite, countably infinite, or uncountable. Justify your...
5. For each set below, say whether it is finite, countably infinite, or uncountable. Justify your answer in each case, giving a brief reason rather than an actual proof. a. The points along the circumference of a unit circle. (Uncountable because across the unit circle because points are one-to-one correspondence to real numbers) so they are uncountable b. The carbon atoms in a single page of the textbook. ("Finite", since we are able to count the number of atoms in...
Please show how answer is derived. Assume the information below to answer the following questions:​ (1)...
Please show how answer is derived. Assume the information below to answer the following questions:​ (1) If you use covered interest arbitrage for a 90-day investment, what will be the amount of US dollars you will have after 90 days? (2) What is the percentage gain or loss on an annual basis? Amount of investment $5,000,000 Current spot rate of pound 1.28 90-day forward rate of pound 1.25 3-month deposit rate in US 2% 3-month deposit rate in UK 3%
Subject: Statistics Please show complete work for the multiple-choice questions below 1. If the mean and...
Subject: Statistics Please show complete work for the multiple-choice questions below 1. If the mean and median are equal, you know that the: a. distribution is symmetrical b. distribution is skewed c. distribution is normal d. mode is equal to the median 2. The mean, median and mode are all measures of: a. the midpoint of the distribution b. the most common score c. percentile ranks d. variability 3. Which of the following characterizes the mean? a. The sum of...
Question 1 - Infinite Sequences. (a). Determine an infinite sequence that satisfies the following . ....
Question 1 - Infinite Sequences. (a). Determine an infinite sequence that satisfies the following . . . (i) An infinite sequence that is bounded below, decreasing, and convergent (ii) An infinite sequence that is bounded above and divergent (iii) An infinite sequence that is monotonic and converges to 1 as n → ∞ (iv) An infinite sequence that is neither increasing nor decreasing and converges to 0 as n → ∞ (b). Given the recurrence relation an = an−1 +...
Below Statement is True, False, or Uncertain question. Justify the response. (Include Graph). Its a Macro...
Below Statement is True, False, or Uncertain question. Justify the response. (Include Graph). Its a Macro economics question Suppose the aim of the government is to increase the economic well-being of it’s citizens. According to the Solow-Swan model from lectures, the government should try to increase the savings rate, as this will lead to a higher steady-state level of capital and a higher level of steady-state outpur, and thus will improve economic well-being
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT