Question

Give the cardinality of the set. (If the set has cardinality No, enter ALEPH NULL.)
{44, 45, . . . , 189, 190}

Answer 1

its still gonna be 190-44+1 .... unless there is something im missing

Answer 2

That's the answer?

Answer 3

...... is what the answer?

Answer 4

190-44+1?

Answer 5

yep

Answer 6

you might wanna actually do the math on it tho ....

Answer 7

So how did you get that?

Answer 8

I'm sorry, I'm just having a difficult time understanding this section :/

Answer 9

let me show you on something more doable ... ok?

Answer 10

Okay

Answer 11

suppose we had the set {4,5,6,7,8} , the cardinality of a set just tells us how many terms are in it.

how many terms do you count in this set?

Answer 12

5

Answer 13

good, now what happens when we try to find the range of this set; lets subtract the first term from the last term: 8-4 = ?

Answer 14

4

Answer 15

as we can see, 4 is not 5 is it? so we need to add 1 to adjust for it right?

Answer 16

Yes

Answer 17

so lets try your set:

{44, 45, . . . , 189, 190}

do you see now where i get the 190, the 44, and why i would add 1 to it all?

Answer 18

Yes

Answer 19

good :) then the cardinality of your set is; 190 - 44 + 1

Answer 20

Okayy, my teacher has us do this n+1 thing?

Answer 21

n just means "some number" usually the last number in the set

Answer 22

Can we go through another example so I can be sure?

Answer 23

yep

Answer 24

{16,20,24,...,400,404}
1) subtract 404 from 16 correct?

Answer 25

this one is trickier, do you see why?

Answer 26

because you add 4 right?

Answer 27

correct, how would you adjust for that?

Answer 28

404-16+4?

Answer 29

lol ... i wish; lets try to work it out on something smaller.

Answer 30

Okay :/

Answer 31

{4,6,8,10,12} ,this adds by 2 right?

Answer 32

and we know theres 5 terms

Answer 33

Correct

Answer 34

12 - 4 = 8 + 2= 10/2 = 5 maybe? but thats just guessing ... lets try it out on something that is by 3s

{4,7,10,13,16} 16-4 = 12+3 = 15/3 = 5 ... looks good so far

Answer 35

7-4 = 3+3 = 6/3 = 2 .... it seems to work to me

Answer 36

last - first + difference
-------------------- = cardinality
difference

Answer 37

Yes

Answer 38

lets try yours now :)

Answer 39

Okay :)

Answer 40

{16,20,24,...,400,404} ; added by 4

404 - 16 + 4
------------ = cardinality then would you agree?
4

Answer 41

98?

Answer 42

101-4 = 97 + 1 = 98; yes

Answer 43

Where did you get 101 from?

Answer 44

404/4 = 101

16/4 = 4

and 4/4 = 1

Answer 45

i just divided it all out first then summed it up

Answer 46

in the end, i did it the same way you did

Answer 47

i see another method we could have used; but its not as straight forward as this one

Answer 48

in order to get the set itself; we could have used the formula:

A(n) = 16 +4(n-1); where "n" tells us the number of terms

Answer 49

How did you get the 101?

Answer 50

\[\frac{404-16+4}{4}=\frac{404}{4}-\frac{16}{4}+\frac{4}{4}=101-4+1\]

Answer 51

i seperated the sumation into individual parts and reduced to work with smaller numbers

Answer 52

A(n) = 16 +4(n-1) ; and we know the last term = 404 soo...

404 = 16 +4(n-1)

404 - 16 = 4(n-1)


404 - 16
-------- = n -1
4


404 - 16
-------- + 1 = n
4


hunh ... its the same formula we worked out above ...

Answer 53

Okay so the cardinality would be 98?

Answer 54

yes, 98 is correct

Answer 55

How would I know if a set had cardinality ALEPH NULL?

Answer 56

Im unsure about the Alpha Null thing

Answer 57

id have to look up the terminology, but i think it means its either infinite and cant be counted, or its empty and cant be counted

Answer 58

Aleph-Null bottles of sode on the wall, Aleph-Null bottles of pop, Take one down, and pass it around, Aleph-null bottles of soda on the wall ....

" The set theory symbol "Aleph-Null" refers to a set having the same cardinal number as the "small" infinite set of integers."

Answer 59

in other words, when the set has infinite terms