Question

Is the set of whole numbers the same as the set of positive integers? Explain.

Answer 1

it depends on your definitions,

is zero in the set?

Answer 2

A number without fractions is a whole number: 0,1,2,3,4,5.......

Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5,...

Answer 3

@UnkleRhaukus these are my definitions :

A. No; the set of positive integers includes 0 but the set of whole numbers does not.
B. Yes; both sets start at 1 and continue into infinity.
C. No; the set of whole numbers includes 0 but the set of positive integers does not.
D. Yes; both sets start at 0 and continue into infinity.

Answer 4

whole numbers are 1,2,3.......
integers are 0,1,2,3........

Answer 5

some definition of whole numbers includes zero some definitions do not

Answer 6

@UnkleRhaukus i dont think whole numbers includes zero in some definitions

Answer 7

are u here @UnkleRhaukus

Answer 8

here?

Answer 9

A set of whole number always includes zero

Answer 10

The integers is the set
\[ \mathbb{Z} = \{...,-2,-1,0,1,2,...\} \]

Answer 11

If zero is removed then it becomes set of natural numbers

Answer 12

@UnkleRhaukus and @uzumakhi

Answer 13

Here's my reasoning:

1) 0 is not in the set of positive integers.
2) Why would anyone bother to create two different sets with the same elements? Think about it!

Answer 14

No, the naturals are the set
\[ \mathbb{N} = \{0,1,2,...\} \]

Answer 15

0 is \(neither\) positive nor negative..

Answer 16

C. No; the set of whole numbers includes 0 but the set of positive integers does not.

Answer 17

^ thats the correct answer

Answer 18

@sauravshakya zero is present in natural numbers

Answer 19

@uzumakhi *no*

Answer 20

No. @uzumakhi

Answer 21

@uzumakhi Nuh-uh.

Answer 22

The positive integers are
\[ Z^+=\{1,2,...\} \]
The whole number is simply the same as the integers, which includes the negatives and zero.

Answer 23

Zero is present in whole numbers. --> correction

Answer 24

Looks like you gotta read more set theory. Eh? @dape That's right.

Answer 25

"+" signifies the absence of zero.\[\mathbb{R}^{+} \implies \text{Set of reals excluding zero.}\]

Answer 26

So, \(\mathbb{R}^{+}\) is the solution in,\[{0 \over x} = 0\]We may say that \(x \in \mathbb{R}^{+}\)

Answer 27

Wow. I just started a lecture on Set Theory. lol

Answer 28

i think C is correct

Answer 29

Usually "*" specifies the absence of zero (or more generally, the origin), and "+" specifies the part greater than zero, so that for example
\[ \mathbb{R}^+=\{x\in\mathbb{R}|x>0\} \]
and
\[ \mathbb{C}^*=\mathbb{C}-\{0\}\]

Answer 30

hmm

Answer 31

@uzumakhi So u got it?