Can there be a largest prime within the concept of infinity?

In summary, the conversation discussed whether infinity is even or odd, with the conclusion that it is neither as it is not a numerical value. It was also mentioned that infinity is not a number that can be used in arithmetic. Other topics included the possibility of a largest prime, the concept of infinity in mathematics, and the gender of elements such as hydrogen and potassium. The discussion then shifted to exploring the idea of using infinity as a prime number, with a link provided for further reading.
  • #1
Icebreaker
Is infinity even or odd? If it's even (or both), then it would mean there's a finitely largest prime.

By coarsely applying limit concepts, and lim(x->inf)x/2 does not yield a remainder.
 
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  • #2
I'm no math Phd, but I do know this: infinity is not a number!
 
  • #3
Infinity isn't a number; it's a concept used in mathematics.
 
  • #4
So, what, we can assume that there will ALWAYS be larger primes?
 
  • #5
You shouldn't assume anything in math. I seem to remember seeing a proof of that somewhere, but I can't remember any of the details. My memory could be wrong. Surely somebody will know though...
 
  • #6
Suppose there are finitely many primes. Can you find a number divisible by all of them? Can you find a number not divisible by any of them?
 
  • #7
Interesting. Is hydrogen male or female? The answer is similar.
 
  • #8
Hurkyl said:
Suppose there are finitely many primes. Can you find a number divisible by all of them? Can you find a number not divisible by any of them?

Wouldn't the question be: suppose there are finitely many primes, can a combination of their products be used to construct any integer?
 
  • #9
Can you find a number not divisible by any of them?

Would the answer to this answer your version?
 
  • #10
infinity = 2 times infinity, hence infinity is even, which may seem odd. :tongue2:
 
  • #11
It's even odder since infinity=2*infinity+1, hence it's odd as well as even. (joking :tongue2:)

Seriously though, infinity is not a number that you can perform arithmetic with. You can add it to the reals and make what's often called the extended reals, but don't expect it to play nice with the rest of the numbers. Certainly don't expect it to have any nice properties like even or odd.
 
  • #12
Hurkyl said:
Would the answer to this answer your version?

What is the answer?
 
  • #13
Not every number can be formed from a product if primes if there were only a finite number of them: multipply them all together and add 1.
 
  • #14
Icebreaker said:
What is the answer?

The answer is yes. If you can find a number not divisible by all the primes, then you would have found a number that is not a combination of their products.

Suppose their are finitely many primes, [itex]p_1,p_2,\ldots,p_n[/itex]. Then consider their product [itex]M=p_{1}p_{2}\ldots p_{n}[/itex]. Then M is divisible by all the primes. This answers Hurkyl's first question (from post#6). Can you use it to answer the second?

edit:I type slower than matt!
 
  • #15
Icebreaker said:
Is infinity even or odd? If it's even (or both), then it would mean there's a finitely largest prime.

By coarsely applying limit concepts, and lim(x->inf)x/2 does not yield a remainder.
In another thread on this forum I've seen posts claiming that an integer cannot be infinite (ie only finite integers are allowed).

See https://www.physicsforums.com/showthread.php?p=478006#post478006

Any thoughts on this subject anyone?

If an infinite integer is allowed, then it must also have an infinite number of digits, right?
 
  • #16
They aren't elements of [tex]\mathbb{Z}[/tex] or [tex]\mathbb{N}[/tex] by definition so your argument is baseless.

You are saying: if we assume that when cantor said the natural numbers he actually meant something entirely different then his argument is wrong. As he didn't mean something entirely different his argument is correct and you are wrong.
 
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  • #17
infinity is a description not a numerical value and since only numerical values can be odd or even, infinity is neither.
 
  • #18
Is green even or odd? Is salt even or odd? Is Fred even or odd? (Oops, bad example, Fred is definitely odd!)

The point is that "infinity" is not a member of the set of integers and that is all the terms "even" or "odd" (in the mathematical sense) apply to.
 
  • #19
If infinity could be reguarded as a number, I think it would e both. It would also be the only number bigger, smaller and the same size as itself at the same time. This is because infinity is not a number. If we were to fill infinity with the highest known number, it would still fall short. Therefore infinity would have to e flled with every impossible number (including decimals). That is the only way it would come close to becoming a "proper" number.
 
  • #20
Chronos said:
Interesting. Is hydrogen male or female? The answer is similar.

Hydrogen is kind of like "Pat What's That".

Potassium, on the other hand, is male, while Chlorine is female.
 

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  • #21
Mmmm so... electronegative...

- Warren
 
  • #22
Actually my original question was badly formulated. My question was about whether there can be a largest prime. I approached the problem by asking can any arbitrarily large number can be divided by 2, and somehow got infinity entangled. It was indeed the wrong approach.
 
  • #23
great idea infinity is a prime number
 
  • #24

Q: What does it mean for infinity to be even or odd?

Infinity is a concept that represents something that has no limit or end. Therefore, it cannot be categorized as even or odd in the traditional sense. It is considered neither odd nor even because it is not a finite number that can be divided into smaller, equal parts.

Q: Can infinity be divided by two?

No, infinity cannot be divided by two. As mentioned before, infinity is not a finite number and it cannot be divided into smaller, equal parts. In other words, infinity cannot be divided at all because it is an abstract concept that denotes something without limit.

Q: Is infinity an even number because it can be divided by 2 an infinite number of times?

No, being divisible by 2 an infinite number of times does not make a number even. In fact, any number can be divided by 2 an infinite number of times and still have a remainder. For example, 1/2 = 0.5, 0.5/2 = 0.25, 0.25/2 = 0.125, and so on. Therefore, infinity cannot be categorized as even or odd based on its divisibility by 2.

Q: If infinity cannot be categorized as even or odd, then what is its parity?

Infinity is not assigned a parity because it is not a finite number and does not follow the same rules as finite numbers. Parity refers to whether a number is even or odd, but since infinity is not a number in the traditional sense, it does not have a parity.

Q: Is there a way to conceptualize infinity as even or odd?

No, infinity cannot be conceptualized as even or odd. As mentioned before, infinity is not a finite number and does not follow the same rules as finite numbers. It is an abstract concept that denotes something without limit, and therefore, cannot be categorized as even or odd.

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