Mock test Mathematics Q2

[Chinmay Bhobe]

how is the N(natural numbers) a subset of Z(integers)

it has to be a proper subset right as per the defination because N is not equal to Z so they are proper subsets and not subset

Thank you

[rakesh ky]

BECAUSE ALL NATURAL NUMBER CAN BE IN INTEGERS ...NATURAL NUMBERS STARTS FROM  {1, 2, 3, ...}  AND INTEGERS FROM = { ..., −4, −3, −2, −1, 0, 1, 2, 3, 4, ... }   

[Pragati Mungekar]

Even I feel that Natural Numbers is Proper Subset of Integers.

All Natural Numbers can be expressed as Integers but still Natural Numbers will never contain the Negative Component of Integers.

Hope we get some clarification on this.

Thanks & Regards,

Pragati.

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[Chinmay Bhobe]

exactly N has all the elements of Z so by the defination N becomes only proper subset of Z and not subset of Z.

May be i have got the whole idea of the difference between Subset and proper subset wrong.

Can anyone please explain to me their exact defination please

Thank you

[DHARMA TEJA GODUMALA]

A is part of B means  =>  A is subset of B

I.e Every element in A is also present In B.

A is subset of A ,

A is not proper subset of A  .

Natural Numbers is Subset of Integers that will be True as every element of N belongs to Z.

Natural Numbers is proper subset of Integers will be true as Set Z contains more elements than N.

Example

A={1,2,3,4,5}

B={1,2)

then B is Subset of A

But In Specific  B is proper subset of A.

In general Every proper subset is also a subset but not every subset is proper subset.

[Chinmay Bhobe]

Thank you...understood