It might sound stupid, but I didn't even realize that could happen (until now...).

]]>(I'm certainly thinking of my younger self when I say this)

This reminds me of "By his bootstraps" and "The man who folded himself"...

]]>Very good! Glad your brother helped.

]]>.

It need not be a person. Certain animals have a concept of numbers and counting.

And numbers, (counting numbers, for instance) have their own existence independent

of human thought. Before there were humans to think about numbers,

there were always places where there was one thing, two things, etc.That's very interesting. If it's true, I don't think it changes my argument;

But which animals did you have in mind?

just substitute 'some animals including humans' for 'person'.

Certain chimpanzees

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This is not a correct example of "a rule that doesn't always work,"

as you put it. You're comparing apples and oranges. Those movements equal

a total of 7 miles walked. The rule works. Mixing in where someone ended

up relative to the starting point is changing the subject.

I was trying to simplify the idea that the rules for, say, vectors, are not the rules for arithmetic. You have supported my argument by demonstrating that one needs to be clear of the circumstances before applying a blanket rule . And ...

You have made a blanket statement. It is not so where x = 0.

Under that method,

<bits of code lost here>

So 0^0 could equal 1,

<bits of code lost here>

Here again you have shown that mathematicians may select their own rules to fit what they want to use them for.

You could make an axiom that 1 = 2. Plus all the usual rules.

It wouldn't be long before you found that the whole number system collapses down to a single number, 1, and a single binary operation, say, times.

Thus you would end up with 1 x 1 = 1. True but somewhat limited in application.

That's my point. You can make up the rules and explore where it leads. If it has use then others will want to use it too.

It need not be a person. Certain animals have a concept of numbers and counting.

And numbers, (counting numbers, for instance) have their own existence independent

of human thought. Before there were humans to think about numbers,

there were always places where there was one thing, two things, etc.

That's very interesting. If it's true, I don't think it changes my argument; just substitute 'some animals including humans' for 'person'. But which animals did you have in mind?

If all humans (and the animals of the above paragraph) were to disappear from the Universe there would still be one thing and two things etc. Yes, but where is the concept of 'three'. You need an intelligence to conceive a 'three'. I still claim it has no independent existence.

Bob

]]>reconsideryouranswer wrote:

but it could equal other values as well.

It can be indeterminate, undefined or 1. Those are the ones that are consistent and make sense with all branches of math.

]]>but three doesnt exist except in the mind of a mathematically inclined person.

It need not be a person. Certain animals have a concept of numbers and counting.

And numbers, (counting numbers, for instance) have their own existence independent

of human thought. Before there were humans to think about numbers,

there were always places where there was one thing, two things, etc.

bob bundy wrote:

So, in certain circumstances, its ok to say 3 + 4 = 7.

But, notice this rule doesnt always work. If I walk 3 miles and then walk 4 miles,

I'm not necessarily 7 miles away from where I started.

This is not a correct example of "a rule that doesn't always work,"

as you put it. You're comparing apples and oranges. Those movements equal

a total of 7 miles walked. The rule works. Mixing in where someone ended

up relative to the starting point is changing the subject.

bob bundy wrote:

So, for instance, when we make the rule for powers:

we find it works ok with all the other stuff we know about powers.

Then when someone poses the question I wonder if we can find a sensible meaning for:

the answer is, yes, we can. It makes good sense to let it have the value 1 because this

is consistent with the rule of powers:

You have made a blanket statement. It is not so where x = 0.

Under that method,

So 0^0 could equal 1,

]]>

Nothing unreal exists!

Jean Dieudonné wrote:

The number 3 exists, because I can immediately see 3 apples. The number 10^10 is an abstraction. It is ridiculous to say I know what 10^10 is. It only has the meaning I give it through the axiomatic system.

Dr. Mifune wrote:

I am not a madman, Mwhahahahahah...

Darn! I am going to get the last word in on one of these .999999999999...., 7.77777777777...,6.6666666666...., 3.333333333333...., 0.00000000000..., ∞.∞∞∞∞∞∞∞∞∞∞..., discussions. I will achieve victory by writing a lengthy rebuttal in the old style. No one will be able to get through it and I will win.

Begin rant:

This kind of stuff is only a bother to the topologists, analysts and logicians who worry about infinity all the time. They suffer with Tarski's paradox, with who cuts whose hair, catalogs of catalogs that do not list themselves, or do and they need two different frameworks to keep set theory afloat. Do we have the axiom of choice today or should we leave it out? Is the continuum hypothesis, true, false? No it is undecidable. Bah, humbug!

To us computational boys this is fine:

Compute 10 / 3 to 16 digits.

3.333 333 333 333 333

Compute 10 / 3 to 25 digits.

3.333 333 333 333 333 333 333 333

Compute 10 / 3 to 31 digits.

3.333 333 333 333 333 333 333 333 333 333

Compute 10 / 3 to hundreds of digits.

3.333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333

Notice the lack of ... on the end of any of them. Fellas, that is what 10 / 3 is if that is all you have time or space for to compute. Remember T. Planiha.

We do not think about what is on the end of that...

To the discretists infinity is the largest number that can currently fit in your computer. See the work of David Deutsch or Doron Zeilberger. Look up DZ's vid on transfinite numbers. If you see it you are in for a shock. A quantum computer type said I was too full of infinity and those 3 dots to understand it. Now, I have been called full of a lot things but never infinity. Those are fighting words where I come from so he is dead but he may have been right.

Doron Zeilberger wrote:

Euclid ruined mathematics.

In the book "1984," Orwell sought to banish thoughtcrime by reducing the language to the point where incorrect thought was impossible.

The discretists ( begins with Kummer ) seek to eliminate the controversy in mathematics by eliminating the need for infinity, continuous math, or even an axiomatic system.

End rant:

(my guess is they will just pass it up and ignore it)

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