- Brian Wilson wrote --
>

Jeffery Hodges commented --

>When I was teaching mathematics in ... class, we were exploring the

>idea of negative numbers using a "number-line" .... We were discussing

>the key idea that a negative number (however far away from zero) is

>smaller than any positive number, this being indicated under the

>number-line by an arrow labelled "smaller" pointing in the direction

>from positive to negative. Above the number-line, another arrow

>labelled "greater", pointed in the opposite direction. Peter correctly

>observed that since -3 = -1 + -2, and, since -3 is the smallest number

>of these, that therefore the whole (-3) is ***smaller*** than one of

>its parts (-1).

>

>

Jeffery,

>The boy was very clever, but there's a sense in which the number -3 is

>greater than either of the parts -2 or -1. If -3 signifies the amount

>of my debt, then my whole debt is larger than either of the parts -2 or

>-1.

>

Yes, but this is not in a mathematical sense. It is true

mathematically that -3 < -1 , but it is false that -3 > -1 , otherwise

mathematics grinds to a halt.>

Not merely on the student's reasoning, but on the definition of smaller

>Strange things happen with negative numbers, I guess. The number -3

>also has the "parts" -4 and +1. Here, one part (-4) is -- on your

>student's reasoning -- smaller and the other (+1) larger.

>

and greater laid down by the system of maths being used. The statement

-4 < -3 is true. It is true also that +1 > -3. Any number "to the left"

of another number on the number-line is smaller, by definition. And any

number "to the right" of another number on the number-line is greater,

by definition. This is not strange. It is normal. It does indeed follow

that, since -3 = -4 + 1, that the whole (-3) is greater than one of its

parts (-4) and smaller than another of its parts (+1), but that actually

confirms my point that the statement that the whole is greater than any

one of its parts is not even true, let alone self-evidently true.

To come back to the subject of this thread, Leonard Maluf and I seem to

be agreed that it is not self-evident that any synoptist redacted his

source material in his own way. I would suggest that the earlier

introduction by someone else of the idea of "self-evident" redaction by

each synoptist has been shown to be very much an irrelevance. I have

enjoyed the excursus into mathematics, but maybe it would not be

appropriate to continue with this on Synoptic-L?

Best wishes,

BRIAN WILSON

>HOMEPAGE http://www.twonh.demon.co.uk/

Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK

> "What can be said at all can be said clearly; and whereof one cannot

_

> speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".

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List Owner: Synoptic-L-Owner@... > >Strange things happen with negative numbers, I guess. The number -3

Just because you apply a bad definition of "is a part of" as

> >also has the "parts" -4 and +1. Here, one part (-4) is -- on your

> >student's reasoning -- smaller and the other (+1) larger.

> >

> Not merely on the student's reasoning, but on the definition of smaller

> and greater laid down by the system of maths being used. The statement

> -4 < -3 is true. It is true also that +1 > -3. Any number "to the left"

> of another number on the number-line is smaller, by definition. And any

> number "to the right" of another number on the number-line is greater,

> by definition. This is not strange. It is normal. It does indeed follow

> that, since -3 = -4 + 1, that the whole (-3) is greater than one of its

> parts (-4) and smaller than another of its parts (+1), but that actually

> confirms my point that the statement that the whole is greater than any

> one of its parts is not even true, let alone self-evidently true.

pointed out by Leonard just before. I do not know exactly if

Leonard is or not a mathematician, but I feel quite confident

with his logic, first with the Goldbach conjecture, and now

with the example of negative numbers.

Leonard wrote :> When I said before that the subject and predicate have to be

The main equivocity is the use of set vocabulary in arithmetic.

> clearly understood as a prerequisite for seeing the truth of a

> self-evident proposition, I meant, among other things, the removal

> of all such equivocities, and hence too, clarity regarding the question

> of "what paradigm of thought is being used", as you describe it.

When you consider sets, for instance {1,2,a,b}, you may say it

is greater than all its parts, for instance {1,b}.

This property does not make sense when applied to arithmetic

(or you should define the way to go from sets to arithmetic)

a+

manu

PS : I know this is not the regular list to post this, and more over

Leonard answered before almost all what would have been to said about.

But I add one precision : the name of the property about even numbers

expressed as sum of two prime numbers is called "Goldbach conjecture",

and is known for more than three century, without having been demonstrated.

Not really self evident.

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