/sci/ - Science & Math

[Anonymous No.5276665]

Need help with the basics of set theory

U = {1,2,3,4,5,6 . . .} let U be the set of all positive integers

A = {1,4,9,16,25, 36, 49, 64, 81}
{x^2 | x ∈ U /\ x^2 < 100}

Why is it that the latter part of the notation has x^2 < 100 and not x^2 <= 81? I understand that 10^2 is 100 and by using your initiative you can deduce that the set A goes up to 9^2 instead but yeah, my question for this one is why not have x^2 <= 81 in the latter of the notation.

Second question
Using the same example as above:
U = {1,2,3,4,5,6 . . .} let U be the set of all positive integers

A = {1,4,9,16,25, 36, 49, 64, 81}
{x^2 | x ∈ U /\ x^2 < 100}

The first x in the notation just before the such that, | , am I right in assuming that that value refers to the number we are working with in the universe? So if I were to write
U = {1, 2, 3, 4, 5, 6, 7}
A = {9, 15 }
{ (x + 2) * 3 | x ∈ U /\ (x + 2) * 3 < 21}

This isn't me asking you guys to do my homework for me just incase it gets to that. I simply need help understand this stuff so I can confidently apply it to other questions.

[Anonymous No.5276669]

bump pls

[Anonymous No.5276670]

> Why is it that the latter part of the notation has x^2 < 100 and not x^2 <= 81?
I don't see how it could possibly matter.

> so if I were to write...
So if you were to write...

[Anonymous No.5276673]

I've got a basic calc question. find ln root ab, a is 5 b is 3

then differentiate ln x^8 ln x, why is in not x^7?

[Anonymous No.5276675]

>>5276670
So what you're saying is that it doesn't matter, the latter part of the notation?

The following example was what I was referring to when I said "So if I were to write"

[Anonymous No.5276679]

>>5276675
> So what you're saying is that it doesn't matter, the latter part of the notation?
Right. I don't think there is any guarantee anyone has made you that sets have unique definitions.

> The following example was what I was referring to when I said "So if I were to write"
I understood what it was supposed to refer to, but not what it was asking.

[Anonymous No.5276680]

>>5276673
OP here and i'm a first year in uni and I can tell you with my level of incompetence I probably won't be of any help. The only relation I see is that 5 + 3 = 8.

inb4 fuck off

[Anonymous No.5276686]

>>5276679
What is that you were asking?

[Anonymous No.5276685]

>>5276680
well ab is multiplication, so im preety sure its 15. i just dont know what to do after that.

[Anonymous No.5276687]

>>5276679
Also thanks for clearing that up for me

[Anonymous No.5276698]

>>5276673
Is the question asking us to find the root of ab, differentiate between x^8 then show why it's not x^7 or was the latter of the question what you're asking?

[Anonymous No.5276705]

>>5276698
its two different questiions

i thot x^7 was the answer, but it isnt. basic calculus, i just cant figure out the answers

and its find ln root ab

[Anonymous No.5276710]

>>5276686
I do not understand what your second question is supposed to be.

[Anonymous No.5276718]

>>5276705
I've yet to do calculus so I don't think i'd be able to help.

What does In root involve doing? If you could give me the formula if there is one I could try see if I can answer your question

[Anonymous No.5276721]

>>5276710
Ah I was just saying is the following correct?

U = {1, 2, 3, 4, 5, 6, 7}
A = {9, 15 }
{ (x + 2) * 3 | x ∈ U /\ (x + 2) * 3 < 21}

Just want to check that my adaptation of the knowledge is correct

[Anonymous No.5276762]

>>5276721
the definition does not correspond to {9,15}. Your definition gives {9 12 15 18}

[Anonymous No.5276820]

>>5276721
{x + (x + 1)) * 3 | x ∈ U /\ (x + (x + 1)) * 3 < 21}

After this duration of minutes it took me to get it right which i'm not happy about, i'm sure this is right.

Amiright guise?

[Anonymous No.5276847]

>>5276820
that works

Please understand that what we're discussing in general here is

{ (element function) where [ criterion conjunction criterion conjunction ... criterion ] }

There is no necessarily relation between what the result and how it is selected.

So
U = { 1 2 3 4 }
Define A = { x | x in U, and x odd }
A= { 1 3 }
Define B = {2x | x in U, and x odd }
B = { 2 6 }
Define C = {x | x in U, and 2x odd }
C = { }
Define D = {x | x in U, and (x odd or x=4)}
D = { 1 3 4 }

[Anonymous No.5276868]

>>5276820
>>5276847
which in other words might be
{ f(x) | subset }
The right side selects some subset of U according to the criteria. The left side applies the function to each element.