0
Answer by piousbox. A previous answer, saved below after "-=-----5", is incorrect. The step that is incorrect is "surely since 1 ele of N and M is UB then (M-1) is ele of N". Why? Suppose that upper limit of N is 5, that is, 5 is in N, but 6 is not. I take M = 9. M is an upper bound of N by definition, and M-1 = 8 is still not in N, still an upper bound of N. The correct solution must involve the notion of *least* upper bound, which involves the notion of completeness (dedekind completeness):
1. Suppose N is bounded above
2. By Dedekind Completeness, there is a minimum upper bound of N, call it m
3. if n is in N then n+1 is in N, and n+1 <= m
4. n <= m-1
5. previous implies that m is not the least upper bound, reaching a contradiction.
-=-----5
sps there was then get a contradiction
what does it mean for N to be bounded above? (u write this defn urself using those cool math symbols)
surely 1 is ele of N therefore for N is not empty
therefore N is bounded Above
let M be an UB (write this meaning out w/ math symbols)
surely since 1 ele of N and M is UB then (M-1) is ele of N
there there exist n ele in N st n is strictly greater than that difference
so then
bring that -1 over to the other side of the inequality, hence n+1 is strcitly greater than M. HEY but wait one sec there buddy cause that's a contradiction of M UB on N
by defn nothing in N is strictly greater than M UB by the simple def of what it means to b UB ( on any set, but in this case the N)
there fore it is not the case that N is bounded above by M ( or by anthing for that matter)
therefore it is the case that N is not bounded above
u need to write this out using those really cool math symbols that you love all too much
Wiki User
∙ 12y ago
Add your answer:
Earn +20 pts
What is natural number 1?
bend over and ill show you
Integer and natural number are equivalent sets if equivalent show that?
They are not equivalent sets.
Show that the natural set of numbers is an unbounded set?
Here is a correct proof by contradiction. Assume that the natural numbers are bounded, then there exists a least upper bound in the real numbers, call it x, such that n ≤ x for all n. Consider x - 1. Since x is the least upper bound, then x - 1 is not an upper bound; i.e. there exists a specific n such that x - 1 < n. But then, x - 1 < n implies x < n + 1, hence x is not an upper bound. QED This concludes the proof; i.e. there exists no upper bound in the real numbers for the set of natural numbers. P.S. There exists sets in which the set of natural numbers are bounded, but these are not in the real number system.
What portion of an angular fracture bounded granitic block sHow is the highest rate of weathering?
edges and corners
What evidence might show two people bounded in there frindship?
When there are comfortable with eachother. When they express themselves without restrained.
Can you show a picture of a quadrilateral shape?
No, because this browser is rubbish. But it is closed plane (flat) shape bounded by four straight lines.
How do you explain to find the remainder for 37 divided by 9?
4.1111
Show a map of where Israel is located?
Israel is located at the extreme eastern end of the Mediterranean Sea, and is bounded by Lebanon, Syria, Jordan, and Egypt.
Do landline phone bills show the number and.or the time you talked?
Yes, phone bills should show the deatails of any charges above basic telephone service charges.
In scansion a is placed above unimportant words?
In scansion, the letter "a" is placed above unimportant words to indicate that they should be pronounced with a reduced emphasis or as unstressed syllables. This helps to show the natural rhythm and stress patterns in a line of poetry.
What is the largest number in natural number?
Numbers can go on and on forever, but most people use ∞ to show infinity, which also means endless.They are endless, but the biggest number is 9 that goes forever.the largest known natural number is a killilionDefinition- million^googolseptplex^G6!^Grahams number=Killilionand the largest useful known number with -illion at the end that is used is a NovemcentillionDefinition- thousand^112 or the 109tg number the the system
What are all the names of a polygons and show a picture of it above the name?
There are an infinite number of different polygons, and some have them have more than one name.
