1
00:00:01,045 --> 00:00:04,992
we are asked 'what number set does the number 8 belong to?'

2
00:00:04,992 --> 00:00:06,733
so this is actually a good review of the different

3
00:00:06,733 --> 00:00:09,311
sets of numbers we often talk about

4
00:00:09,311 --> 00:00:12,051
so the first set under consideration is

5
00:00:12,051 --> 00:00:13,733
the natural numbers

6
00:00:13,733 --> 00:00:17,067
natural numbers

7
00:00:17,067 --> 00:00:19,533
and these are essencially the counting numbers

8
00:00:19,533 --> 00:00:22,732
and you're not and not counting 0,

9
00:00:27,547 --> 00:00:30,714
1, 2, 3, so on and so forth

10
00:00:30,933 --> 00:00:32,879
so clearly 8 is a natural number,

11
00:00:32,879 --> 00:00:36,455
you can count up to 8 here, you can count 8 objects

12
00:00:36,455 --> 00:00:40,867
so 8 is a member of the natural numbers

13
00:00:40,867 --> 00:00:42,933
so it is a natural number, we should say

14
00:00:44,733 --> 00:00:46,164
the next one we should consider,

15
00:00:46,533 --> 00:00:49,180
let's consider the whole numbers

16
00:00:49,180 --> 00:00:54,474
whole numbers, right over here

17
00:00:54,474 --> 00:00:57,267
and i should say natural numbers

18
00:00:57,267 --> 00:00:58,839
so let's consider the whole numbers

19
00:00:58,839 --> 00:01:03,205
the whole numbers are essencially the same thing as the

20
00:01:03,205 --> 00:01:06,200
natural numbers, but we're now going to include the 0

21
00:01:06,200 --> 00:01:11,517
so it's 0, 1, 2, 3, so on and so forth

22
00:01:11,517 --> 00:01:13,793
so clearky 8 is one of these as well

23
00:01:13,793 --> 00:01:17,044
you could eventually increment your way to 8 like here

24
00:01:17,044 --> 00:01:18,669
just counting all of the whole numbers

25
00:01:18,669 --> 00:01:21,734
another way to view this is the non-negative numbers

26
00:01:21,734 --> 00:01:24,800
so 8 clearly belongs to this as well

27
00:01:24,800 --> 00:01:28,468
so let's expand our set a little bit, let's think about integers

28
00:01:28,468 --> 00:01:31,533
let's think about the set of integers

29
00:01:31,533 --> 00:01:34,800
now these are all the numbers starting with

30
00:01:34,800 --> 00:01:37,267
well, you could keep counting down, but all the way up to

31
00:01:37,267 --> 00:01:45,790
-3, -2, -1, 0, 1, 2, 3 and you could just keep going there

32
00:01:45,790 --> 00:01:48,200
now clearly 8 is one of these as well, you can just keep

33
00:01:48,200 --> 00:01:50,388
counting to 8, in fact, you can

34
00:01:50,388 --> 00:01:52,199
let me just put a check box there and

35
00:01:52,199 --> 00:01:55,775
in general, you have the integers that contain

36
00:01:55,775 --> 00:01:58,190
both the positive and the negative numbers

37
00:01:58,190 --> 99:59:59,999
and the 0