# Thread: how is possibill demonstring ?

1. ## Re: how is possibill demonstring ?

If n is a natural number >= 3, I think your proof is logically acceptable, but its format may not be. That depends on how formal your proofs must be.
A more formal proof might look like:

Assume there exists a natural number k such that k >= 3 and there exists a pair of natural numbers, a[sub:2hgzwvdo]k[/sub:2hgzwvdo] and b[sub:2hgzwvdo]k[/sub:2hgzwvdo], such that (a[sub:2hgzwvdo]k[/sub:2hgzwvdo] + b[sub:2hgzwvdo]k[/sub:2hgzwvdo] + 1) = k.
Let a[sub:2hgzwvdo]k+1[/sub:2hgzwvdo] = a[sub:2hgzwvdo]k[/sub:2hgzwvdo].
So, a[sub:2hgzwvdo]k+1[/sub:2hgzwvdo] is a natural number.
Let b[sub:2hgzwvdo]k+1[/sub:2hgzwvdo] = b[sub:2hgzwvdo]k[/sub:2hgzwvdo] + 1.
So, b[sub:2hgzwvdo]k+1[/sub:2hgzwvdo] is a natural number.
(a[sub:2hgzwvdo]k+1[/sub:2hgzwvdo] + b[sub:2hgzwvdo]k+1[/sub:2hgzwvdo] + 1) = [a[sub:2hgzwvdo]k[/sub:2hgzwvdo] + (b[sub:2hgzwvdo]k[/sub:2hgzwvdo] + 1) + 1] = [(a[sub:2hgzwvdo]k[/sub:2hgzwvdo] + b[sub:2hgzwvdo]k[/sub:2hgzwvdo] + 1) + 1] = (k + 1).
And (k + 1) is a natural number >= 3.
So, (k + 1) is a natural number >= 3 such that there exists a pair of natural numbers, a[sub:2hgzwvdo]k+1[/sub:2hgzwvdo] and b[sub:2hgzwvdo]k+1[/sub:2hgzwvdo], such that (a[sub:2hgzwvdo]k+1[/sub:2hgzwvdo] + b[sub:2hgzwvdo]k+1[/sub:2hgzwvdo] + 1) = (k + 1)
If there exists a natural number k such that k >= 3 and there exists a pair of natural numbers, a[sub:2hgzwvdo]k[/sub:2hgzwvdo] and b[sub:2hgzwvdo]k[/sub:2hgzwvdo], such that (a[sub:2hgzwvdo]k[/sub:2hgzwvdo] + b[sub:2hgzwvdo]k[/sub:2hgzwvdo] + 1) = k,
then, for every natural number n >= k, there exists a pair of natural numbers, a[sub:2hgzwvdo]n[/sub:2hgzwvdo] and b[sub:2hgzwvdo]n[/sub:2hgzwvdo], such that a[sub:2hgzwvdo]n[/sub:2hgzwvdo] + b[sub:2hgzwvdo]n[/sub:2hgzwvdo] + 1 = n.
Let a[sub:2hgzwvdo]3[/sub:2hgzwvdo] = 1, which is a natural number.
Let b[sub:2hgzwvdo]3[/sub:2hgzwvdo] = 1, which is a natural number.
(a[sub:2hgzwvdo]3[/sub:2hgzwvdo] + b[sub:2hgzwvdo]3[/sub:2hgzwvdo] + 1) = 3, which is a natural number >= 3.
THUS, for every natural number n >= 3, there exists a pair of natural numbers, a[sub:2hgzwvdo]n[/sub:2hgzwvdo] and b[sub:2hgzwvdo]n[/sub:2hgzwvdo], such that a[sub:2hgzwvdo]n[/sub:2hgzwvdo] + b[sub:2hgzwvdo]n[/sub:2hgzwvdo] + 1 = n.

2. ## Re: how is possibill demonstring ?

- ... sorry but you have wrote it first time that k is a natural number greater or equal 3 and ... little later you write that k+1 is greater or equal 3 too ...

sorry but i think that this is not possible ?

3. ## Re: how is possibill demonstring ?

Originally Posted by jhonyy9
- ... sorry but you have wrote it first time that k is a natural number greater or equal 3 and ... little later you write that k+1 is greater or equal 3 too ...

sorry but i think that this is not possible ?
4 is greater than OR equal to 3, correct?
5 is also greater than or equal to 3.

If I had said k = 3, then I could not say (k + 1) = 3.
But if I say k > 3, then I can say (k + 1) > 3.

The "or" makes all the difference.

Make sense?

4. ## Re: how is possibill demonstring ?

.... thank you for your reply , so yes this i understand but check please in your sentence ,,Assume there ... " you have wrote that k is greater or equal 3 .... so after with 3- 4 line you write that k+1 is greater or equal 3 too ...

- pardon but i think that this is error,this is not possible ...

5. ## Re: how is possibill demonstring ?

4 > 3 so 4 >= 3
5 > 3 so 5 >= 3.

6. ## Re: how is possibill demonstring ?

ok thank you very much ... now i have understood it ... thank you !

7. ## Re: how is possibill demonstring ?

- sorry - can you tel me how is possible a with down k - sorry but i not can know how is possible writing how you have wrote - being equal with a down k+1 ...- or this is really possible when b down k not is equal with b down k+1 ?

8. ## Re: how is possibill demonstring ?

Originally Posted by jhonyy9
- sorry - can you tel me how is possible a with down k - sorry but i not can know how is possible writing how you have wrote - being equal with a down k+1 ...- or this is really possible when b down k not is equal with b down k+1 ?

Your question is excellent. Unfortunately, the difference in our native languages may prevent my giving you an understandable explanation.

Do you know what a "set" is? If not, please look it up in a dictionary.
As an example of a set, let's think of the weights of the students in a class.
Let's say there are thirty students in the class.
So, we name or label each student's weight with a number from 1 to 30. This is the first student's weight. This is the second student's weight. And so on.
Understand so far?
So, w[sub:u0f3w79s]1[/sub:u0f3w79s] is the notation for the first student's weight. The w stands for the weight; the 1 describes the student. w[sub:u0f3w79s]2[/sub:u0f3w79s] is the notation for the second student's weight. The "down" as you call it (a subscript is the technical term and is derived from the Latin meaning "written below") identifies which student is being discussed. Can two different students have the same weights? Sure they can. Can the same two students have different heights even though they weigh the same? Sure they can.

I apologize if this explanation makes no sense to you. It may be better to have someone who is conversant in mathematics and speaks your native language explain it.

PS To make a "down" remember that it is called a "subscript." In the toolbar above where you write, you will see a button called sub. If you want to make a subscript, highlight what you want subscripted and push the sub button.

PPS An "up" is called a "superscript," from the Latin for "written above." See the button marked "sup" right beside the "sub" button.

PPPS You said above "I not can know." This is not good English. In English, verbs are most usually expressed as a modal plus a main verb. Example. He can go. The modal is in blue; the main verb is in red. Other examples. He did go. He will go. He was going. To negate these statements, it is usual to place "not" between the modal and the main verb. So to negate these examples, you say: He can not go. He did not go. He will not go. He was not going.

9. ## Re: how is possibill demonstring ?

- so thank you very much ... you are one good teacher ... hope you will help me in my next problems too ... because i think that may be ...

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