True by definition? "If 3 is an integer, and three is greater than zero, then 3 is a positive integer."

[PseuTonym]

I think that zero is not a real number. It only indicates absence of anything.

How about the number 130?

I think that the zero indicates that the number 130 is a multiple of ten.
In particular, 130 = (13 times 10).

Now, consider ten itself:
10 = 1+1+1+1+1+1+1+1+1+1
There doesn’t seem to be an absence of ones when we write 10 in ordinary Hindu-Arabic decimal notation.

Now, consider the absence of a numerator.
Do we have (0/100) = (/100)?
It’s not clear what value a fraction has when the numerator is omitted.
It looks like a syntax error.

 

[STT]

How about the number 130?

I think that the zero indicates that the number 130 is a multiple of ten.
In particular, 130 = (13 times 10).

Now, consider ten itself:
10 = 1+1+1+1+1+1+1+1+1+1
There doesn’t seem to be an absence of ones when we write 10 in ordinary Hindu-Arabic decimal notation.

Now, consider the absence of a numerator.
Do we have (0/100) = (/100)?
It’s not clear what value a fraction has when the numerator is omitted.
It looks like a syntax error.

Zero in all case you mentioned is a symbol. Think of 1+0=1.

 

[PseuTonym]

Zero in all case you mentioned is a symbol.

I don’t see your point. The addition sign “+” is a symbol. The equals sign “=” is a symbol. The Hindu-Arabic sign for three (“3”) is a symbol. So what?

I was responding to your claim that zero “only indicates absence of anything.”

13 = thirteen
130 = (13 times 10) = (thirteen times ten)

The symbol “0” written after “13” indicates that we are to multiply the number thirteen by the number ten.

“Multiplied by ten” isn’t an absence. It’s the application of the operation of multiplication by the particular value ten.

 

[PseuTonym]

Think of 1+0=1.

Why are you adding? Your claim is about zero: " It only indicates absence of anything."

You didn’t specify that, “When you are adding, and the symbol zero stands alone as something to be added …”

Consider (5 times 2 times 100 times 0) = 0
(Surely you didn’t expect 1000? Multiplying by zero can have an effect.)

Consider (130 + 130) <-----The zeroes stand for “times 10.”
(130 + 130)
= ((13 times ten) + (13 times ten))
= ((13 + 13) times ten)
= (26 times 10)
= 260

 

[Tomdstone]

How about the number 130?

I think that the zero indicates that the number 130 is a multiple of ten.
In particular, 130 = (13 times 10).

Correct, of course, as we learn in grammar school arithmetic class.
Also, for your original question, it seems to be quite trivial because any integer greater than zero is a positive integer.

 

[PseuTonym]

Correct, of course, as we learn in grammar school arithmetic class.

Are you indicating that you would have brought that example to the attention of STT, and that I didn’t need to bother? Or are you suggesting that STT should simply be ignored?

Also, for your original question, it seems to be quite trivial

My train of thought began in response to an allegedly reliable general principle that was invoked to arrive at a conclusion, and the claim of triviality was already made at the beginning.

Look here:
Why should we waste any more time on such trivialities?

Tomdstone, please be aware that you are already convinced of something and that you raise the objection “trivial” because my efforts seem to be overkill. However, from the point of view of some other people, the triviality is a sign that I should not be raising questions, and that I am supposed to accept what I was told.

Would you have responded to STT’s claims (“I think that zero is not a real number. It only indicates absence of anything”) by simply saying that the matter is trivial and that STT is wrong? I would imagine that STT could respond by saying that the matter is trivial and STT is right.

I already proposed two advantages of focus on what is agreed to be trivial:
[1. The less knowledge required, the greater the number of people who can understand and participate in the discussion.

1. If I provide a very clear and simple counter-example to a claim (and I mean clear and simple ideas, not attitudes), then it doesn’t merely serve to gain approval from people who are on “my side” in a debate, but has a chance of actually influencing the beliefs of my opponent in the debate.
   ](http://forums.catholic-questions.org/showpost.php?p=14339701&postcount=373)

 

[STT]

I don’t see your point. The addition sign “+” is a symbol. The equals sign “=” is a symbol. The Hindu-Arabic sign for three (“3”) is a symbol. So what?

I was responding to your claim that zero “only indicates absence of anything.”

13 = thirteen
130 = (13 times 10) = (thirteen times ten)

The symbol “0” written after “13” indicates that we are to multiply the number thirteen by the number ten.

“Multiplied by ten” isn’t an absence. It’s the application of the operation of multiplication by the particular value ten.

We have a zero which indicate no amount and another zero which is a symbol. Let me give you two examples: (1) “0” which means no amount and (2) “zero” which appears at the end of 10 and it is a symbol to show 10 in base ten.

 

[Tomdstone]

…the claim of triviality was already made at the beginning.

So we agree that it is a trivial matter.