Discret Math

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describe function mins that takes a non-empty of natural numbers for its argument, and has the smallest natural number in the set for its value.

i tried to use the function min which takes two integers as arguments and has the smaller of them for its value
but could not form it all together correctly Sad

Help please??

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View best answer, chosen by AlaaAL

@AlaaAL,

AlaaAL wrote:

i tried to use the function min which takes two integers as arguments and has the smaller of them for its value
but could not form it all together correctly

Help please??

Min (x, y) := (x +y - |x-y|)/2

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@AlaaAL,

Oh, I misunderstood. Hang on...

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@AlaaAL,

AlaaAL wrote:

describe function mins that takes a non-empty of natural numbers for its argument, and has the smallest natural number in the set for its value.

Define the set function "min (S)" recursively as follows using the binary function "min(x, y)" from my earier post that takes two integers as arguments:

(I) if S has one element y, let min (S) = y;
(II) otherwise, if S is finite choose some x in S, and let min (S) = min (x, min (S - {x}));
(III) otherwise, S is infinite, so choose some x in S and let min (S) = min ({ y in S such that y <= x}).

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@Kolyo,

Thanks for clarifying things for me! when you break it down its seems easier.
can i ask for one more question
if i want to write down in axiomatic description
for example:
absolute value of an integer:
abs : Z →Z
∀n : Z •
n ≤0⇒abs n = - 􀀀n
n ≥0⇒ abs n = n

i'm finding it confusing for me, could you help me with that please?

1 Reply

@AlaaAL,

AlaaAL wrote:

Thanks for clarifying things for me! when you break it down its seems easier.

Glad I could help at least somewhat.

Quote:

if i want to write down in axiomatic description
for example:
absolute value of an integer:
abs : Z →Z
∀n : Z •
n ≤0⇒abs n = - 􀀀n
n ≥0⇒ abs n = n

i'm finding it confusing for me, could you help me with that please?

I'm afraid I don't understand what you're asking for here (or even what the • after the Z means! Smile

)

Do you want me to do for my set-function "min" what you've done for "abs"?

If so, it would probably look something like this:

minimium value of a non-empty set of natural numbers:
min: P(ℕ)\{Ø} --> ℕ
∀ S ϵ P(ℕ)\{Ø},
∀ x ϵ S,
|S| = 1 ⇒ min(S) = x
1 < |S| < ∞ ⇒ min(S) = min(x, min(S\{x}))
|S| = ∞ ⇒ min(S) = min({y ϵ S | y ≤ x})

I want to stress that I am NOT an expert in this stuff.
Think of me as a fellow student, not as a professor who knows all the answers.

1 Reply

@Kolyo,

This question has a little bit of math and software engineer that's why you maybe got confused , i apologize for not clearing this up firstly in my original question.

I really appreciate your help Smile

Thanks.

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