Question

prove that (0,∞) is uncountable.[hint:e^x]

Proof requires clear logic, clear writing, because English is not your mother tongue

Answer #1

Which of the following sets are finite? countably infinite?
uncountable? Give reasons for your answers for each of the
following:
(a) {1\n :n ∈ Z\{0}};
(b)R\N;
(c){x ∈ N:|x−7|>|x|};
(d)2Z×3Z
Please answer questions in clear hand-writing and show me the
full process, thank you (Sometimes I get the answer which was
difficult to read).

Prove the following equivalencies by writing an equivalence
proof (i.e., start on one side and use known equivalencies to get
to the other side). Label each step of your proof to explain the
equivalency.
A ∨ B → C ≡ (A → C) ∧ (B → C)
A → B ∨ C ≡ (A → B) ∨ (A → C)

Prove that f(x)=x*cos(1/x) is continuous at x=0.
please give detailed proof. i guess we can use squeeze
theorem.

Please clear writing
and explain step by step this should be a simple question
Explain your knowledge and use proper math notation and
explain
Consider the function
f : [0,1]→R deﬁned by (f(x) =0 if x = 0) and (f(x)=1 if 0
< x≤1)
(i)Compute L(f)
andU(f).
(ii) Is f Riemann
integrable on [0,1]?

PLEASE SHOW ALL WORK IN A CONCISE PROOF WILL GIVE A LIKE:
Prove g(x)=x^3 is an injective map. Why does the argument in
your proof not work the map h(x)=x^2?

Discrete Maths ( Please use a concise and clear
explanation as well because these I tend to get confused with these
kind of question like which quantifiers to use and also the
placement of the paranthesis)
Statements with nested quantifiers: English to logic, part
2.
The domain for the variables x and y are the set of musicians in
an orchestra. The predicates S, B, and P are defined as:
S(x): x plays a string instrument
B(x): x plays a...

You will write a program that loops until the user selects 0 to
exit. In the loop the user interactively selects a menu choice to
compress or decompress a file. There are three menu options: Option
0: allows the user to exit the program.
Option 1: allows the user to compress the specified input file
and store the result in an output file.
Option 2: allows the user to decompress the specified input file
and store the result in an...

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