help with writing maths Watch

#maths
Badges: 0
Rep:
?
#1
Report Thread starter 5 years ago
#1
I need help with a few questions. I've copied the questions and my attempts at them.

1) Turn words into symbols, using standard or Zermelo definitions (or any other symbolic representation).

  • The set of rational points in the open unit cube

I've done this: \{(x,y,z)\in\mathbb{Q}: 0<x,y,z<1\} but it looks wrong to me.

2) For each item, provide
(i) a coarse description, which only identifies the class to which
the item belongs (set, function, polynomial, etc.);
(ii) a finer description, which defines the object in question, or
characterises its structure


  • (1, 1 + x, 1 + x + x^2, 1 + x + x^2 + x^3, . . .)

sequence, an infinite sequence with increasing terms (is this the right way of wording this?!)

  • 13 = (3 + 2√−1)(3 − 2√−1) Is this just a quadratic expression?




  • \sum\limits_{k=1}^\infty \frac{1}{k^2 + x^k}

an infinite sum of fractions with increasing degree...?

Sorry for all the questions. A bit of help would be appreciated!
0
quote
reply
ghostwalker
  • Study Helper
Badges: 15
#2
Report 5 years ago
#2
(Original post by #maths)
  • The set of rational points in the open unit cube

I've done this: \{(x,y,z)\in\mathbb{Q}: 0<x,y,z<1\} but it looks wrong to me.
A rational point is a point whose coordinates are rational. The ordered triplet is not a rational number.

Have another go.
quote
reply
#maths
Badges: 0
Rep:
?
#3
Report Thread starter 5 years ago
#3
(Original post by ghostwalker)
A rational point is a point whose coordinates are rational. The ordered triplet is not a rational number.

Have another go.
I know a point with rational coordinates would be z=(x,y)\in Q^2

and the unit cube is [0,1]^3

but I don't know how to put them together,

the set of rational points in the open unit cube is \{z \in Q: 0<z<1\} this is obviously wrong
0
quote
reply
ghostwalker
  • Study Helper
Badges: 15
#4
Report 5 years ago
#4
(Original post by #maths)
I know a point with rational coordinates would be z=(x,y)\in Q^2
As you noticed the ordered pair (x,y) is not a rational number, it cannot be an element of Q.

BUT it can be an element fo Q^2 - as you posted.

So, just extend that to three coordinates. You're only missing the exponent in your original post.
quote
reply
BlueSam3
Badges: 17
Rep:
?
#5
Report 5 years ago
#5
(Original post by #maths)
I know a point with rational coordinates would be z=(x,y)\in Q^2

and the unit cube is [0,1]^3

but I don't know how to put them together,

the set of rational points in the open unit cube is \{z \in Q: 0<z<1\} this is obviously wrong
That's the one dimensional version (the open unit interval (0,1)). You have already posted the two dimensional version (the open unit square (0,1) \times (0,1)) You want the three dimensional analogue. You were very close at the start.
0
quote
reply
maths2015
Badges: 1
Rep:
?
#6
Report 3 years ago
#6
We're struggling with the same questions this year. Can you help us please?
1
quote
reply
ghostwalker
  • Study Helper
Badges: 15
#7
Report 3 years ago
#7
(Original post by maths2015)
We're struggling with the same questions this year. Can you help us please?
Post details of what you've done/tried and where you're stuck.
quote
reply
maths2015
Badges: 1
Rep:
?
#8
Report 3 years ago
#8
Name:  image.jpeg
Views: 205
Size:  85.9 KB
Is this correct?
0
quote
reply
Zacken
Badges: 22
Rep:
?
#9
Report 3 years ago
#9
(Original post by maths2015)
Name:  image.jpeg
Views: 205
Size:  85.9 KB
Is this correct?
Nopes, why would (x, y, z) \in \mathbb{Q}^2 be true? Wrong exponent.
0
quote
reply
maths2015
Badges: 1
Rep:
?
#10
Report 3 years ago
#10
Would it be Q^3 instead?
0
quote
reply
Zacken
Badges: 22
Rep:
?
#11
Report 3 years ago
#11
(Original post by maths2015)
Would it be Q^3 instead?
Yups!
1
quote
reply
maths2015
Badges: 1
Rep:
?
#12
Report 3 years ago
#12
Thank you so much!
0
quote
reply
maths2015
Badges: 1
Rep:
?
#13
Report 3 years ago
#13
Another question: {x∈R\Q : x2 ∈N} in words.

* Set x is a set of irrational numbers such that x^2 are natural numbers.
Is this correct?
0
quote
reply
Zacken
Badges: 22
Rep:
?
#14
Report 3 years ago
#14
(Original post by maths2015)
Another question: {x∈R\Q : x2 ∈N} in words.

* Set x is a set of irrational numbers such that x^2 are natural numbers.
Is this correct?
I don't see anything wrong with it.
0
quote
reply
maths2015
Badges: 1
Rep:
?
#15
Report 3 years ago
#15
Question:
For each item, provide two levels of description: (i) a coarse de- scription, which only identifies the class to which the item belongs (set, function, polynomial, etc.); (ii) a finer description, which defines the object in question, or characterises its structure

Name:  image.png
Views: 172
Size:  771 Bytes
For this question can we write 'infinite sequence with increasing terms,?
0
quote
reply
BlueSam3
Badges: 17
Rep:
?
#16
Report 3 years ago
#16
(Original post by maths2015)
Question:
For each item, provide two levels of description: (i) a coarse de- scription, which only identifies the class to which the item belongs (set, function, polynomial, etc.); (ii) a finer description, which defines the object in question, or characterises its structure

Name:  image.png
Views: 172
Size:  771 Bytes
For this question can we write 'infinite sequence with increasing terms,?
Not necessarily increasing: What about the case x = -1?
0
quote
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19

Were you ever put in isolation at school?

Yes (170)
27.11%
No (457)
72.89%

Watched Threads

View All