How do you know you are not "A.I."?

[viole]

I would say, logically speaking, they are equal. But don't you appreciate the fancy math I did? I added a zero to infinite zeros. I'm special like that.

Yes, very special.

And if they are equal, then it is a solution to

X/10 = X.

How many solutions does that equation have, in your opinion? (Please note, it can be seen as the intersection of two straight lines, both passing through the origin.

Y = X
Y = X/10

What does your geometric intuition tell you?

Ciao

- viole

 

[Acim]

No, they can be merely hypotheses.
But regarding the function of numbers, extensive experience with their usefulness gives confidence thru inductive reasoning, rather than faith.
Btw, "faith", as I use it here, is believing in things unverifiable & unfalsifiable.

The hypotheses require (some degree of) faith.

After that faith (in whatever) is accepted as (great) starting point, then the following points/conclusions and usefulness may be (further) substantiated by faith and reasoning.

I am using faith to mean: complete trust or confidence in someone or something (or what my computer's dictionary and I imagine most dictionaries say in conveying the definition of faith)

 

[Acim]

Yes, very special.

And if they are equal, then it is a solution to

X/10 = X.

How many solutions does that equation have, in your opinion? (Please note, it can be seen as the intersection of two straight lines, both passing through the origin.

Y = X
Y = X/10

What does your geometric intuition tell you?

Ciao

- viole

I was very poor at geometry, in terms of equations. But I could try anyway.

I'm not understanding what you are asking. Please clarify.

 

[viole]

The hypotheses require (some degree of) faith.

After that faith (in whatever) is accepted as (great) starting point, then the following points/conclusions and usefulness may be (further) substantiated by faith and reasoning.

I am using faith to mean: complete trust or confidence in someone or something (or what my computer's dictionary and I imagine most dictionaries say in conveying the definition of faith)

I am afraid not.

Conclusions can be true, without the premise being true. That works only for sufficient and necessary conditions.

For instance, if a=2 and b=2 then a+b=4. But that does not entail that if a+b=4 then a= 2 and b= 2.

Ciao

- viole

 

[Revoltingest]

The hypotheses require (some degree of) faith.

There's no need to believe.....only to assume.

After that faith (in whatever) is accepted as (great) starting point, then the following points/conclusions and usefulness may be (further) substantiated by faith and reasoning.

Again, no faith is needed.
Consider how it differs from religion, which requires belief in something unverifiable.
It typically boils down to some book or some preacher saying something....& that something is to be believed as inerrant truth.
Math is easily verified by anyone.
You can conduct experiments with bacon strips to show: 2 + 2 = 4

I am using faith to mean: complete trust or confidence in someone or something (or what my computer's dictionary and I imagine most dictionaries say in conveying the definition of faith)

To trust on the basis of repeated verification is a more metaphorical use of "faith".
But in this sense, I'm almost OK with it.

 

[Acim]

I am afraid not.

Conclusions can be true, without the premise being true. That works only for sufficient and necessary conditions.

For instance, if a=2 and b=2 then a+b=4. But that does not entail that if a+b=4 then a= 2 and b= 2.

Ciao

- viole

The a+b=4 and a is not (necessarily) 2 and b is not (necessarily) 2, would be reasoning. I don't see that assertion as being a premise.

 

[viole]

I was very poor at geometry, in terms of equations. But I could try anyway.

I'm not understanding what you are asking. Please clarify.

Ok. No geometry,either. I am sorry to say that, but I wonder why you venture in math if you do not even know how to find the intersection of two straight lines in terms of cartesian equations.

Ok. Another shot at it.

Then, please tell me which number can possibly be equal to itself when divided by 10.

Ciao

- viole

 

[viole]

The a+b=4 and a is not (necessarily) 2 and b is not (necessarily) 2, would be reasoning. I don't see that assertion as being a premise.

Why not? I am perfectly free to say that a+b=4 is a premise about two unknown numbers.

What prevents me from doing that?

Ciao

- viole

 

[Acim]

There's no need to believe.....only to assume.

Somewhat agree. Faith doesn't require 'belief' anymore than assumptions do.

Again, no faith is needed.
Consider how it differs from religion, which requires belief in something unverifiable.

Disagree with this. Disagree that religion requires belief (could just as easily be an assumption) and disagree that it is inherently unverifiable. Akin to my asking for objective verification of existence of a physical world, without relying on something within that (imagined world) to substantiate itself.

It typically boils down to some book or some preacher saying something....& that something is to be believed as inerrant truth.

Yeah, not for me.

Math is easily verified by anyone.
You can conduct experiments with bacon strips to show: 2 + 2 = 4

Can we construct bacon strip experiments to show .999... equals 1? Ya know, cause it is easily verifiable for anyone?

To trust on the basis of repeated verification is a more metaphorical use of "faith".
But in this sense, I'm almost OK with it.

IMO, you are limiting what faith actually means and then using that limited (or bastardized) version of faith to say it has nothing to do with premises/assumptions. I find that disingenuous. But very okay / forgivable.

 

[Acim]

Why not? I am perfectly free to say that a+b=4 is a premise about two unknown numbers.

What prevents me from doing that?

Ciao

- viole

Nothing. But the assertion that a and b are not necessarily 2 is reasoning (that is also including a degree of faith).

 

[viole]

Nothing. But the assertion that a and b are not necessarily 2 is reasoning (that is also including a degree of faith).

A degree of faith? a can be 1, and b can be 3, and still yield 4.

What faith do I need?

Ciao

- viole

 

[Revoltingest]

Somewhat agree. Faith doesn't require 'belief' anymore than assumptions do.

I think we're using greatly different definitions of the word, "faith".

Disagree with this. Disagree that religion requires belief (could just as easily be an assumption) and disagree that it is inherently unverifiable. Akin to my asking for objective verification of existence of a physical world, without relying on something within that (imagined world) to substantiate itself.

Your views of religion also differ greatly from mine.
it see it as quite different from math & science.

Can we construct bacon strip experiments to show .999... equals 1? Ya know, cause it is easily verifiable for anyone?

That particular example isn't amenable to proof by bacon.
But it is based upon experiments with bacon.

IMO, you are limiting what faith actually means and then using that limited (or bastardized) version of faith to say it has nothing to do with premises/assumptions. I find that disingenuous. But very okay / forgivable.

Be careful accusing others of being disingenuous.

 

[Acim]

A degree of faith? a can be 1, and be can be 3, and still yield 4.

What faith do I need?

Ciao

- viole

- that these things exist (for you)
- that when combined they equal something
- that when combined they equal (exactly) 4
- that a & b are not necessarily some pre-defined (or pre-supposed) quantity

 

[Acim]

I think we're using greatly different definitions of the word, "faith".

Agreed. I'm using the dictionary definition for faith. In one word, I would equate faith to trust. But if then asking to apply that to 'problems' I'm going to rely on faith, but likely to employ reasoning, along the way.

Your views of religion also differ greatly from mine.
it see it as quite different from math & science.

That's fine. I don't know how religion entered the picture other than this is how you choose to limit the definition of faith. I feel I'm coming more from philosophy and getting at foundational notions/conceptions, rather than taking those for granted. I find taking those for granted to be useful for a great many things. Here in this dialogue, I'm not taking them for granted.

Be careful accusing others of being disingenuous.

Be careful on how you use the word faith.

 

[viole]

- that these things exist (for you)
- that when combined they equal something
- that when combined they equal (exactly) 4
- that a & b are not necessarily some pre-defined (or pre-supposed) quantity

Yes, I have faith in the axioms of Peano. I also have faith that bachelors are not married. Among other things. Like 2 being greater than 1.

I think we are digressing. We first need to solve your problem.

You admitted that 0.0000...1 divided by 10 yealds the same number, logically. Now, if we make the assumption that logic is not a matter of faith, , what number can possibly be equal to itself when divided by 10?

Ciao

- viole

 

[LegionOnomaMoi]

Yes, very special.

Actually, our friend has accidentally hit upon something akin to an informal version of the hyperreals.
I have to say I admire the clarity, simplicitly, patience, and just downright brilliance of your pedagogical approach in the past several posts.

 

[Revoltingest]

Agreed. I'm using the dictionary definition for faith.

Do you think there's only one definition?
The definition inferred would depend upon context.
So to say that math requires "faith" is inappropriate at best
Instead of accusing others of being disingenuous, you should first consider if you're creating confusion with clumsy use of language.

 

[Acim]

Yes, I have faith in the axioms of Peano. I also have faith that bachelors are not married. Among other things. Like 2 being greater than 1.

I think we are digressing. We first need to solve your problem.

You admitted that 0.00001 divided by 10 yealds the same number, logically. Now, if we make the assumption that logic is not a matter of faith, , what number can possibly be equal to itself when divided by 10?

Ciao

- viole

Rephrasing so I can understand what is being asked: If we assume logic is not employing any sense of trust in its ability to reason and its conclusions, what number(s) can possibly be equal to themselves when divided by 10?

Perhaps (don't know), numbers that deal with infinity in some fashion?

 

[viole]

Rephrasing so I can understand what is being asked: If we assume logic is not employing any sense of trust in its ability to reason and its conclusions, what number(s) can possibly be equal to themselves when divided by 10?

Perhaps (don't know), numbers that deal with infinity in some fashion?

What about zero?

Ciao

- viole

 

[Revoltingest]

Rephrasing so I can understand what is being asked: If we assume logic is not employing any sense of trust in its ability to reason and its conclusions, what number(s) can possibly be equal to themselves when divided by 10?

Perhaps (don't know), numbers that deal with infinity in some fashion?

Hint:
Basic algebra yields an exact integer answer.