Scientific results here and now apply to there and then

[Ken Rank]

I'm not talking about any fossils. I'm asking if it would be deceptive to create fossils of animals that never lived.

I am not following. Are you saying fossils were created of animals that never lived? I want to understand your point... but if you are saying you aren't talking about any fossils but are then asking if it would be deceptive if God did do such a thing... then you're asking me to answer a hypothetical, right?

 

[JackRT]

I am not following. Are you saying fossils were created of animals that never lived? I want to understand your point... but if you are saying you aren't talking about any fossils but are then asking if it would be deceptive if God did do such a thing... then you're asking me to answer a hypothetical, right?

I have seen posts on these forums from young earth creationists that claimed that dinosaurs never existed.

 

[essentialsaltes]

I am not following. Are you saying fossils were created of animals that never lived? I want to understand your point... but if you are saying you aren't talking about any fossils but are then asking if it would be deceptive if God did do such a thing... then you're asking me to answer a hypothetical, right?

Earlier you wrote: "It isn't deceptive if God creates a man and, when 2 minutes old, the man looks to be 25."

So you claim it is not deceptive for something to be created with an 'appearance of age' as in the Omphalos/Last Thursday hypothesis.

I'm just trying to find out what that means for you.

My view is clear. Certain rocks 'appear' to be 4 billion years old because they are 4 billion years old.

Trilobites appear to have lived and died long before there were any humans on earth.

So some part of the appearance of age of the earth is that there were billions of years of creatures living and dying before humanity arose. If the earth was created 6000 years ago (as many claim) then fossils older than 6000 years are not remains of animals that lived and died.

Maybe you believe in an old earth, and so old fossils aren't a problem.
Maybe you believe trilobites and dinosaurs lived alongside man.
Maybe you believe God created fossils of creatures that never lived, in order to make the earth appear old, but this is not deceptive.
Maybe you believe fossils are deceptions planted by Satan to confuse us.

 

[klutedavid]

The concept of infinity is difficult for the layperson to grasp particularly when they are not familiar with the mathematics.

The concept of infinity is beyond the concept of the finite.

For example there are infinite sets that are countable;

Incorrect.

There are only ever finite sets of countable numbers, countable numbers are always finite numbers.

Let the letter, N, be positive integers say.

N, N+1, N+2, ... are always finite positive integers. Any set of Integers are always defined as finite sets by definition.

there are infinite sets that are uncountable;

That is a contradiction.

You just said, there are finite sets that are not finite sets.

If a set of integers for example, is an uncountable set, then that set of Integers is not a set of integers. Integers are always finite and countable.

the set of positive integers is an infinite set as is the set of integers

A paradox generated by an inconsistent definition.

Finite numbers include all positive integers, all sets of positive integers are always finite.

The concept of infinity is much more complicated than the layperson definition.

Infinity is never defined by the concept of a finite quantity.

The relationship between curvature and infinity can be explained with a relevant analogy; the Riemann curvature scalar R for the surface of a sphere of radius r defined by the equation.
R = 2/r²

Countable numbers are finite numbers and no matter how big the finite number becomes, that finite number by definition, can never be an infinite number. Simple because there is no such thing as an infinite number.

 

[essentialsaltes]

There are only ever finite sets of countable numbers, countable numbers are always finite numbers.

Already, you're proving what sjastro said about people who are "not familiar with the mathematics."

Numbers are not countable. Sets are countable. A set is countable if it can be put in a 1-1 correspondence with the positive integers.

Any set of Integers are always defined as finite sets by definition.

What definition is that?

I say that the set of all integers is infinite. If there were only a finite number of integers, you could name the largest one. Name me the largest integer, and I will agree with you that there are only a finite number of them.

 

[sjastro]

Already, you're proving what sjastro said about people who are "not familiar with the mathematics."

Numbers are not countable. Sets are countable. A set is countable if it can be put in a 1-1 correspondence with the positive integers.



What definition is that?

I say that the set of all integers is infinite. If there were only a finite number of integers, you could name the largest one. Name me the largest integer, and I will agree with you that there are only a finite number of them.

Thanks.
You saved me making a response.

 

[klutedavid]

Already, you're proving what sjastro said about people who are "not familiar with the mathematics."

Numbers are not countable. Sets are countable. A set is countable if it can be put in a 1-1 correspondence with the positive integers.



What definition is that?

I say that the set of all integers is infinite. If there were only a finite number of integers, you could name the largest one. Name me the largest integer, and I will agree with you that there are only a finite number of them.

Finite numbers may refer to:

Countable numbers less than infinity, being the cardinality of a finite set – i.e., some natural number, possibly 0.
(wikipedia)

Please read that definition carefully.

Less than infinity, though infinity is not a numerical entity.

Integers are finite numbers and the set of all positive integers are bounded within that set of finite numbers.

Any number beyond that set of finite numbers, is beyond the domain of mathematics itself.

A largest positive integer is a contradiction of the definition of a finite set and does not exist.

The set of positive integers cannot by definition be an infinite set. Simply because infinity is not a numerical entity.

 

[essentialsaltes]

A largest positive integer is a contradiction of the definition of a finite set and does not exist.

{5, 6, 23, 58} is a finite set. It has a largest element. Finite sets do have a largest element.

The set of all integers is an infinite set. It has no largest element.

The set of positive integers cannot by definition be an infinite set. Simply because infinity is not a numerical entity.

Note that there is an important difference between infinite and infinity. I do not need infinity to be a member of the set of positive integers. Nevertheless, the set of positive integers is infinite.

 

[klutedavid]

{5, 6, 23, 58} is a finite set. It has a largest element. Finite sets do have a largest element.

The set of all integers is an infinite set. It has no largest element.



Note that there is an important difference between infinite and infinity. I do not need infinity to be a member of the set of positive integers. Nevertheless, the set of positive integers is infinite.

Your speaking in two languages at once, a mathematical language of finite numbers. And at the same time using a language consisting of words that are not mathematical.

Infinity is not a numerical entity.

A set of any finite numbers is never an infinite set, because the term 'infinite' is not numerically defined.

I will prove this now.

Consider the set of positive integers, {1,2,3,...}

This set of positive integers contains only positive integers.

Since every single positive integer in that set is always followed by another positive integer. Then that set is by definition is bounded by the finite set of all numbers.

If you were to say, a finite set can be an infinite set. Then that is a paradox.

Mathematics is a discipline concerned with numbers and infinity is not a number.

 

[klutedavid]

Your speaking in two languages at once, a mathematical language of finite numbers. And at the same time using a language consisting of words that are not mathematical.

Infinity is not a numerical entity.

A set of any finite numbers is never an infinite set, because the term 'infinite' is not numerically defined.

I will prove this now.

Consider the set of positive integers, {1,2,3,...}

This set of positive integers contains only positive integers.

Since every single positive integer in that set is always followed by another positive integer. Then that set is by definition is bounded by the finite set of all numbers.

If you were to say, a finite set can be an infinite set. Then that is a paradox.

Mathematics is a discipline concerned with numbers and infinity is not a number.

Your trying to claim that some set of finite numbers, is somehow, an infinite set of finite numbers?

 

[essentialsaltes]

Your speaking in two languages at once, a mathematical language of finite numbers. And at the same time using a language consisting of words that are not mathematical.

Infinity is not a numerical entity.

Great, I haven't really used that word. Only infinite, which is something else.

Since every single positive integer in that set is always followed by another positive integer.

Then there is no end to them. They are infinite.

Finite things have a finish, an end. Infinite things do not.

 

[zippy2006]

Then there is no end to them.

I would definitely bring in a zombie analogy at this point. It's a generational strategy, but it seems to work wonders.

 

[46AND2]

Consider the set of positive integers, {1,2,3,...}

This set of positive integers contains only positive integers.

Since every single positive integer in that set is always followed by another positive integer. Then that set is by definition is bounded by the finite set of all numbers.

No, the set of all positive integers is unbounded.(above, that is; it is bounded by 1 below).

Bounded Sets - Mathonline

As is the set of all real numbers. (above; bounded by 0 below)

 

[sjastro]

Your speaking in two languages at once, a mathematical language of finite numbers. And at the same time using a language consisting of words that are not mathematical.

Infinity is not a numerical entity.

A set of any finite numbers is never an infinite set, because the term 'infinite' is not numerically defined.

I will prove this now.

Consider the set of positive integers, {1,2,3,...}

This set of positive integers contains only positive integers.

Since every single positive integer in that set is always followed by another positive integer. Then that set is by definition is bounded by the finite set of all numbers.

If you were to say, a finite set can be an infinite set. Then that is a paradox.

Mathematics is a discipline concerned with numbers and infinity is not a number.

Your trying to claim that some set of finite numbers, is somehow, an infinite set of finite numbers?

Why don't you pay attention to essentialsaltes' posts instead of making things up.
An infinite set contains an infinite number of elements.
The set of natural numbers N = {0,1,2,3…………….} is clearly an infinite set as is the set of integers Z = {…….-3,-2,-1, 0,1,2,3……….}

An infinite set that is countable means that each element in the set can be mapped from the set of natural numbers by a one-one and onto function.
For example the infinite set of integers Z is countable according to the function f;
f(n) = n/2 where n is even or zero and f(n) = -(n-1)/2 if n is odd; n is an element of N.
There are some very surprising results.
The infinite set of rational numbers Q is countable as a function f can be defined.
The infinite set of real numbers R on the other hand is an uncountable infinite set as no such function f can exist.

The set of prime numbers is an infinite set.
This was proven by the ancient Greeks who used proof by contradiction method where they assumed the set of prime numbers formed a finite set with the largest prime number.
What they found was there always a larger prime number outside this set irrespective of how large they made the finite set.
Hence by contradiction the set of prime numbers is an infinite set.

 

[klutedavid]

{5, 6, 23, 58} is a finite set. It has a largest element. Finite sets do have a largest element.

The set of all integers is an infinite set. It has no largest element.



Note that there is an important difference between infinite and infinity. I do not need infinity to be a member of the set of positive integers. Nevertheless, the set of positive integers is infinite.

You will need to pick me up on that.

Using infinity instead of infinite.

 

[klutedavid]

Great, I haven't really used that word. Only infinite, which is something else.



Then there is no end to them. They are infinite.

Finite things have a finish, an end. Infinite things do not.

Positive integers starting at number one are bounded and cannot be thought of as an infinite set of positive integers. Since an infinite set is unbounded.

Real numbers have no value at zero on a number line. Therefore real numbers also belong to a set that is bounded. An infinite set is unbounded, no start and no finish.

One cannot have an infinite number of real numbers on a number line, that are between two positive integers on that same number line.

The two positive integers on that number line form the bounds of that set of real numbers.

An infinite number is unspecified in mathematics, hence a number line cannot approach an infinite value.

The set of all numbers (Z) cannot be defined as an infinite set, as the set (Z) can never approach an infinite point. Because that point or number is not defined in mathematics.

So it is illogical to say a number line approaches an infinite value, when that very infinite value has no mathematical quantity.

 

[klutedavid]

Why don't you pay attention to essentialsaltes' posts instead of making things up.

I am not the creative one here.

An infinite set contains an infinite number of elements.

An infinite set by definition is a set without bounds. Thus an infinite set cannot exist.

The set of natural numbers N = {0,1,2,3…………….} is clearly an infinite set as is the set of integers Z = {…….-3,-2,-1, 0,1,2,3……….}

Both of these sets are bounded sets. The set of natural numbers starts at zero and has a bound. An infinite set is unbounded.

The set of integers are divided into positive and negative integers, both positive and negative integers are bounded at zero. An infinite set is unbounded.

An infinite set that is countable means that each element in the set can be mapped from the set of natural numbers by a one-one and onto function.
For example the infinite set of integers Z is countable according to the function f;
f(n) = n/2 where n is even or zero and f(n) = -(n-1)/2 if n is odd; n is an element of N.
There are some very surprising results.
The infinite set of rational numbers Q is countable as a function f can be defined.
The infinite set of real numbers R on the other hand is an uncountable infinite set as no such function f can exist.

All numbers no matter how they are defined have a bound.

The set of prime numbers is an infinite set.

Once again, prime numbers have a bound.

This was proven by the ancient Greeks who used proof by contradiction method where they assumed the set of prime numbers formed a finite set with the largest prime number.
What they found was there always a larger prime number outside this set irrespective of how large they made the finite set.
Hence by contradiction the set of prime numbers is an infinite set.

No set of finite numbers can ever be an infinite set. An infinite set is an impossible concept.

 

[essentialsaltes]

Positive integers starting at number one are bounded and cannot be thought of as an infinite set of positive integers.

What is this bound? What is the largest positive integer? There is none, as you have stated: "every single positive integer in that set is always followed by another positive integer"

Since an infinite set is unbounded.

Correct. If there is no biggest positive integer, the positive integers are unbounded.

 

[essentialsaltes]

Once again, prime numbers have a bound.

What is the largest prime number?

---

Suppose there was a largest prime number called P.

Then we could construct a number that was one larger than the product of all of the finite prime numbers.

This number would be 2*3*5*7*11*13*...*P + 1

This number is bigger than P, so it can't be prime (since P is the largest prime). Which means that it must be divisible by smaller primes. But by construction, the remainder when you divide this new number by any prime will be 1. This is a contradiction. Therefore there are not a finite number of primes. The number of primes is infinite.

 

[klutedavid]

What is this bound? What is the largest positive integer? There is none, as you have stated: "every single positive integer in that set is always followed by another positive integer"



Correct. If there is no biggest positive integer, the positive integers are unbounded.

The bound is the number one for all positive integers. An infinite set is unbounded.

What is it that you cannot see here?

Bounded means bounded.

The count of positive integers never approaches an infinite value because that value does not exist as a mathematical value. Thus an infinite set of positive integers is really an undefined set.