# Not everything that is true can be proven

#### Deleted member 115935

Joined Dec 31, 1969
0
So @
nsaspook

where do yo expect this conversation to go ?

As this is not in general chat , I assume it has an end point / objective ?

#### Delta Prime

Joined Nov 15, 2019
1,311
So @
nsaspook

where do yo expect this conversation to go ?

As this is not in general chat , I assume it has an end point / objective ?
Mathematics is one of the only areas of knowledge that can objectively be described as "true," because its theorems are derived from pure logic. And yet, at the same time, those theorems are often extremely strange and counter-intuitive
Euler's Equation reaches down into the very depths of existence.

#### xox

Joined Sep 8, 2017
796
Yes that is one that we always have to keep in mind when comparing results from floating point arithmetic.
So it can be even simpler than that:
2!=2
sometimes.
This is also interesting because sometimes it will print out in a console as "2" when really it is "1.9999999999999999" or something like that. Depends on the print format specifiers being used.
That is why it is good to use an algorithm to compare results.
Exactly.

Code:
#include "float.h"
#include "stdlib.h"

typedef double real;

int real_compare(double lhs, double rhs, double eps) {
if(eps == 0)
eps = DBL_EPSILON;
double dif = lhs - rhs;
if (abs(dif) <= eps)
return 0;
if (dif < 0)
return dif < eps ? -1 : 1;
return dif > eps ? 1 : -1;
}

#define real_same(lhs, rhs, eps) (real_compare(lhs, rhs, eps) == 0)
#define real_less(lhs, rhs, eps) (real_compare(lhs, rhs, eps) < 0)
#define real_same_or_less(lhs, rhs, eps) (real_compare(lhs, rhs, eps) <= 0)
#define real_more(lhs, rhs, eps) (real_compare(lhs, rhs, eps) > 0)
#define real_same_or_more(lhs, rhs, eps) (real_compare(lhs, rhs, eps) >= 0)

#include "math.h"
#include "stdio.h"

int main(int argc, char** argv) {
real two = pow(sqrt(2), 2);
real computed = two + two;
real actual = 4;
printf("computed: %g\n", computed);
printf("actual:   %g\n", actual);
printf("computed == actual: %s\n", computed == actual ? "TRUE" : "FALSE");
printf("real_same(computed, actual, DBL_EPSILON): %s\n",
real_same(computed, actual, DBL_EPSILON) ? "TRUE" : "FALSE");
printf("real_less(computed, actual, DBL_EPSILON): %s\n",
real_less(computed, actual, DBL_EPSILON) ? "TRUE" : "FALSE");
printf("real_same_or_less(computed, actual, DBL_EPSILON): %s\n",
real_same_or_less(computed, actual, DBL_EPSILON) ? "TRUE" : "FALSE");
printf("real_more(computed, actual, DBL_EPSILON): %s\n",
real_more(computed, actual, DBL_EPSILON) ? "TRUE" : "FALSE");
printf("real_same_or_more(computed, actual, DBL_EPSILON): %s\n",
real_same_or_more(computed, actual, DBL_EPSILON) ? "TRUE" : "FALSE");
}
Output:

computed: 4
actual: 4
computed == actual: FALSE
real_same(computed, actual, DBL_EPSILON): TRUE
real_less(computed, actual, DBL_EPSILON): FALSE
real_same_or_less(computed, actual, DBL_EPSILON): TRUE
real_more(computed, actual, DBL_EPSILON): FALSE
real_same_or_more(computed, actual, DBL_EPSILON): TRUE

#### Delta Prime

Joined Nov 15, 2019
1,311
As this is not in general chat , I assume it has an end point / objective ?
It has no end point! Take the number "1" simple right! Wrong! 1= 0.999, followed by an infinite string of nines, is equivalent to one, people don't believe it could be true. The left side represents the beginning of mathematics; the right side represents the mysteries of infinity.

#### Deleted member 115935

Joined Dec 31, 1969
0
It has no end point! Take the number "1" simple right! Wrong! 1= 0.999, followed by an infinite string of nines, is equivalent to one, people don't believe it could be true. The left side represents the beginning of mathematics; the right side represents the mysteries of infinity.
I was meaning as to where this general conversation on anything was going ,
Did the Op have a end point / answer ?

#### Delta Prime

Joined Nov 15, 2019
1,311
I am not that pretentious, to speak for the thread starter. In my opinion.
The subject it's very provocative. encouraging one to ponder deeply.
Something that is unresolved makes it very intriguing to Me! There was a joke offered by Mr. @Yaakov
That put it in a nutshell for me. My interpretation; It's about something you once found interesting but has since been resolved and is no longer of interest to you, so you move on .

#### MrAl

Joined Jun 17, 2014
9,785
So @
nsaspook

where do yo expect this conversation to go ?

As this is not in general chat , I assume it has an end point / objective ?
What are you the thread police all of a sudden?

Some conversations get more interesting as time goes on even if they diverge a little.
We sometimes talk about related things, that's all there is to it.

#### MrAl

Joined Jun 17, 2014
9,785
It has no end point! Take the number "1" simple right! Wrong! 1= 0.999, followed by an infinite string of nines, is equivalent to one, people don't believe it could be true. The left side represents the beginning of mathematics; the right side represents the mysteries of infinity.
I am familiar with that one. It is another interesting view on what infinity is.
Infinity to me is an idea, that something can be so large that it beats out everything else.
To put it in perspective, i like to quote the "Counting to Infinity" exercise, where a man starts to count from 1 to infinity, then as he gets too old his son takes over, then his son, etc., then one of them gets the idea to count by 10's instead of 1's, then by 100's, then 1000's, then billions, etc., then another one gets the idea to get the next number by taking a power, then incrementing the power instead of the number itself, and that leads to power like 10, 100, 1000, etc., same pattern but now it's an exponent. Then the next son gets the idea to use a computer, then a super computer, then the next son uses a faster computer, etc., then the next son starts taking derivatives using that as an indication of what the result would be, and the count goes on and on. It's funny that the speed of the counting is always increasing but it never helps. Even though the method of counting gets faster with each generation it just doesnt matter.

Infinity in real life is an interesting idea. Sometimes we can approximate it and get usable results too, other times we cant approximate it. It also represents some physical impossibilities like infinite distance. We might integrate over a distance from 1 to infinity to get an answer, but in the real universe we see things change as we go farther out that were not included in the calculation, one difference between classical and quantum physics.

#### Deleted member 115935

Joined Dec 31, 1969
0
What are you the thread police all of a sudden?

Some conversations get more interesting as time goes on even if they diverge a little.
We sometimes talk about related things, that's all there is to it.
NO MrAI,

Anything wrong with that ?

Is my view any less relevant than yours ?

#### MrAl

Joined Jun 17, 2014
9,785
NO MrAI,

Anything wrong with that ?

Is my view any less relevant than yours ?
Oh ok, it sounded like you have a problem with conversations that may diverge a little.
Dont get me wrong though, when someone is talking about one thing and someone else butts in and changes the entire conversation to something else entirely different that's annoying. That happens in real life sometimes. You are not done talking about something and someone else tries to change to a totally different subject often unrelated in any way.

#### MrSalts

Joined Apr 2, 2020
2,767
It has no end point! Take the number "1" simple right! Wrong! 1= 0.999, followed by an infinite string of nines, is equivalent to one, people don't believe it could be true. The left side represents the beginning of mathematics; the right side represents the mysteries of infinity.
If that is how you view life, how do you manage to get out of bed, put your pants on and serve yourself any food? Logical masterbation is fun for everyone but at some point, the fun and games stop and a person has to figure out how to feed themselves.

#### djsfantasi

Joined Apr 11, 2010
8,792
It has no end point! Take the number "1" simple right! Wrong! 1= 0.999, followed by an infinite string of nines, is equivalent to one, people don't believe it could be true. The left side represents the beginning of mathematics; the right side represents the mysteries of infinity.
As an undergraduate applied mathematics major, I was taught that 2+2=5, for large values of 2 and small values of 5…

#### MrAl

Joined Jun 17, 2014
9,785
Geometry is part of math but relates math to shapes.
Knowing the geometrical interpretation of some math transform or the other way around and we get a much, much better idea what is going on and exactly why.
Take the transformation between the time domain and the frequency domain. It is just the link between views of a spiral from different angles or more exactly a projection of a spiral onto a single dimension plan.

Mechanics is like geometry in motion. We use that to describe various processes and so we have transformed math into real life, or so we might think at first. We can describe so much with classical mechanics because of years of experiments and observations of what we thought was the end of all that was needed, well, almost.
Unfortunately, that 'almost' is such a huge almost that we find that we missed a lot by thinking that we can use our senses alone and what we thought was the baseline reality. Turns out what we had done in the past was all statistical as we were only seeing the average of a lot of things that were happening, and we didnt see some other things happening because we never saw them in nature or with the experiments up to that point.
Now quantum physics comes along and shows us that reality for us is mostly statistical because that's all we needed to survive up to this point. But surviving this planet will take a deeper look at the physics of the universe or at least everything in it. Some of the stuff is hard to believe and i think that is because of a lot of disinformation brought about by articles that dont really describe the experiments correctly, and that leads people to start to doubt everything they read.

Remember the old adage, "Mathematics is the key to the universe". But you cant open any door that you have not yet seen.

BTW this was an old thread

#### Delta Prime

Joined Nov 15, 2019
1,311
Hello there.Welcome to AAC!
But, I hope I will deal with it
There is an entire community here that will help you "deal with it".
That's for sure! That is why learning math is very difficult for me
You are not alone.

#### dcbingaman

Joined Jun 30, 2021
855
I love "The game of life" - It was one of the original programs that I wrote in C.

I showed my girlfriend at the time and she said that the graphics looked crap - lol
I have a windows version written in C# if you are interested.

#### dcbingaman

Joined Jun 30, 2021
855
Yes. Math has axioms. Axioms are assumed true and generally are taken as true without a proof. English has words, but if you follow the definition of words downward you find a place where the words are defined in terms of other undefined words. This is the base of human language and these types of words are known intuitively in the mind but cannot be defined using other words. Proofs always use axioms that are assumed to be true. You have to start with some assumptions no matter how you look at it.
Then you have 'faith'. Faith is something you take to be true but you cannot prove or disprove it. You personally just 'know' it to be true. Is there life after death? That is a faith question. Everyone has faith in something, if nothing else than at least in the basic axioms that many cannot be proven or disproven. We decide to take them as true without proof.
There is other knowledge we take to be true even though we do not personally have any direct proof ourselves. Example: I know there is a place called 'China' and I know what it looks like from a map, but I have never been there and have no direct proof myself. I have 'faith' that what others have told me about it is true and since so many others confirm it, I take it as true even though I personally cannot prove it or disprove it.

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#### cmartinez

Joined Jan 17, 2007
7,915
Then you have 'faith'. Faith is something you take to be true but you cannot prove or disprove it. You personally just 'know' it to be true.
Very, very well put. Thanks for that. The only thing I'd adjust in your previous statement is that 'faith' (which is akin to a spiritual axiom) is something that I 'accept' as being true without definite solid proof.

How do we know we're not insane and our senses are not deceiving us, making us think this is reality while we're probably living in a simulation? ... the answer is you can never really know ... you just have to accept this reality and move on. Otherwise you're going to waste your life away in a circular problem which can never be solved.

#### nsaspook

Joined Aug 27, 2009
10,925
I'm perfectly fine with a simulation.

#### cmartinez

Joined Jan 17, 2007
7,915
I'm perfectly fine with a simulation.
Then, by all means ... do not ever take the RED Pill!

#### click_here

Joined Sep 22, 2020
545
I have a windows version written in C# if you are interested.
Sure, PM it to me - did you use WPF, or Windows forms?

Not too long ago I rewrote the GoL using dual data types - It was originally just a sparse array, but then I made every element also a member of a linked list to quickly and easily iterate through.

(I was just trying to get some code for a sparse array up and running and GoL is a nice little project that fits the data type well)