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There are five people standing on a line: A, B, C, D and E. Each is asked how
many people standing before them are taller than they are, and the replies from
each were respectively: 0, 1, 1, 0 and 1. Sort these five people according to their
height.
many people standing before them are taller than they are, and the replies from
each were respectively: 0, 1, 1, 0 and 1. Sort these five people according to their
height.
Infinity Roy made an stadium with infinite number of seats. Where all the seats
are numbered as 1,2,3……… For a special guest stadium committee take the
decision to transfer the spectators from nth numbered seat to n+1th numbered seat
For this they refund him{(1÷n)-(1÷(n+1)) } dollar . How many dollar stadium committee needs
to transfer seat by this process
are numbered as 1,2,3……… For a special guest stadium committee take the
decision to transfer the spectators from nth numbered seat to n+1th numbered seat
For this they refund him{(1÷n)-(1÷(n+1)) } dollar . How many dollar stadium committee needs
to transfer seat by this process
Infinity Roy made an stadium with infinite number of seats. Where all the seats
are numbered as 1,2,3……… For a special guest stadium committee take the
decision to transfer the spectators from nth numbered seat to n+1th numbered seat
For this they refund him{(1÷n)-(1÷(n+1)) } tk . How many taka stadium committee needs
to transfer seat by this process.
are numbered as 1,2,3……… For a special guest stadium committee take the
decision to transfer the spectators from nth numbered seat to n+1th numbered seat
For this they refund him{(1÷n)-(1÷(n+1)) } tk . How many taka stadium committee needs
to transfer seat by this process.
Is mathematics dependent upon the notion of reproducibility i.e. experimentation and instantiations? Why or why not?
The growth in the value of a bond is modelled by the equation B(y) = 3000(1 + 0.025)y. What does the 3000 represent?
Tamara is a marine photographer who wants to photograph marine life on a coral reef 21 m below the surface. She knows that the light intensity reduces by 2% for each metre below the water surface. It is a bright, sunny day, so the intensity of light at the surface is 100%.
5.1. Make a detailed critique of the philosophy of empiricism in Mathematics.
5.2. Is Mathematics dependent upon the notion of reproducibility i.e. experimentation and instantiation? Why or why not?
5.2. Is Mathematics dependent upon the notion of reproducibility i.e. experimentation and instantiation? Why or why not?
4.1. How does Mill’s empiricism differ from Quine’s empiricism? Which one, to you, appears to be more appealing? Why?
4.2. What does Butterworth’s experiment about one-day old babies learning arithmetic show you? Is this evidence for or against empiricism?
4.3. Do you agree that mathematical truths derived from logical deductions are more “true” than ones based on empirical observations? Why or why not?
4.2. What does Butterworth’s experiment about one-day old babies learning arithmetic show you? Is this evidence for or against empiricism?
4.3. Do you agree that mathematical truths derived from logical deductions are more “true” than ones based on empirical observations? Why or why not?
3.1. Russell’s paradox discovered by Bertrand Russell in 1901, showed that the naive set of theory of Frege leads to a contradiction.
It might be assumed that, for any formal criterion, a set exists whose members are those objects (and only those objects) that satisfy the criterion; but this assumption is disproved by a set containing exactly the sets that are not members of themselves. If such a set qualifies as a member of itself, it would contradict its own definition as a set containing sets that are not members of themselves. On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition. This contradiction is Russell’s paradox.
HOW WOULD YOU EXPLAIN THIS PARADOX TO YOUR STUDENTS? HOW CAN YOU ESCAPE FROM THIS PARADOX?
It might be assumed that, for any formal criterion, a set exists whose members are those objects (and only those objects) that satisfy the criterion; but this assumption is disproved by a set containing exactly the sets that are not members of themselves. If such a set qualifies as a member of itself, it would contradict its own definition as a set containing sets that are not members of themselves. On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition. This contradiction is Russell’s paradox.
HOW WOULD YOU EXPLAIN THIS PARADOX TO YOUR STUDENTS? HOW CAN YOU ESCAPE FROM THIS PARADOX?
2.1. Discuss the continuum hypothesis of Georg Cantor. What does Godel say about his hypothesis? What does Paul Cohen say about this hypothesis and the axiom of choice of Zermelo and Fraenkel?
2.2. Is there a set of numbers whose cardinality is greater than the cardinality of the integers but which is less than the cardinality of the reals?
2.2. Is there a set of numbers whose cardinality is greater than the cardinality of the integers but which is less than the cardinality of the reals?
