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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'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?
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?
The concept of infinity is beyond the concept of the finite.The concept of infinity is difficult for the layperson to grasp particularly when they are not familiar with the mathematics.
Incorrect.For example there are infinite sets that are countable;
That is a contradiction.there are infinite sets that are uncountable;
A paradox generated by an inconsistent definition.the set of positive integers is an infinite set as is the set of integers
Infinity is never defined by the concept of a finite quantity.The concept of infinity is much more complicated than the layperson definition.
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.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
There are only ever finite sets of countable numbers, countable numbers are always finite numbers.
Any set of Integers are always defined as finite sets by definition.
Thanks.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: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.
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.
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.{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.
Since every single positive integer in that set is always followed by another positive integer.
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.
Why don't you pay attention to essentialsaltes' posts instead of making things up.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?
You will need to pick me up on that.{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.
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.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.
I am not the creative one here.Why don't you pay attention to essentialsaltes' posts instead of making things up.
An infinite set by definition is a set without bounds. Thus an infinite set cannot exist.An infinite set contains an infinite number of elements.
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 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……….}
All numbers no matter how they are defined have a bound.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.
Once again, prime numbers have a bound.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.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.
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.
Once again, prime numbers have a bound.
The bound is the number one for all positive integers. An infinite set is unbounded.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.
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