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Is infinity an odd or even number? (2011)

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Re: Is infinity an odd or even number? (2011)

#361

Post by MichaelMoser123 »

pclmulqdq wrote: post #358
MichaelMoser123 wrote: post #338

Earlier quoted context omitted.

Also: in javascript you can divide by zero > 1/0 Infinity But python throws a divide by zero error: >>> 1/0 Traceback (most recent call last): File " ", line 1, in ZeroDivisionError: division by zero Still you do have infinity and nan in python - because these are part of the floating point spec. >>> float('inf') - float('inf') nan >>> float('inf') == float('inf') True >>> NAN=float('inf') - float('inf') >>> NAN == N…

Dividing by 0 or -0 is a valid floating-point operation because there's an infinity in the number system, and JS uses double precision floating point for all numbers. Python has an integer type and a double type, and division by 0 is disallowed for integers, but okay for doubles.

your explanation makes sense, however python doesn't allow division of floating point number by 0 either:

  >>> type(1.0)
  
  >>> 1.0/0
  Traceback (most recent call last):
    File "", line 1, in 
  ZeroDivisionError: float division by zero
However numpy lets you do it - it is only a warning

  >>> import numpy as np

  >>>
  >>> np.divide(1.0,0)
  __main__:1: RuntimeWarning: divide by zero encountered in    true_divide
  inf

Re: Is infinity an odd or even number? (2011)

#362

Post by operator-name »

bragr wrote: post #301
gowld wrote: post #290

Earlier quoted context omitted.

On the contrary, it's entirely natural. The technical definition is quite intuitive. "There are many infinities! The smallest one is bigger than all the counting numbers, so you can't count up to it, but it's out there! We call it omega . You can make bigger infinities too, like omega + 1!" Kids LOVE that, and it's good math too! (But gets tricky quickly, because addition of transfinite ordinals is not commutative, a…

>On the contrary, it's entirely natural. The technical definition is quite intuitive. https://xkcd.com/2501/

Terminology and strict definitions aside, it is quite intuitive. A commenter below also pointers this out:

> If you ask a child what comes after infinity, "Infinity + 1" is pretty much the default answer. Any kid who knows multiplication knows "Infinity + Infinity" is the same as "Infinity Times Two". The answer of "Infinity TIMES Infinity" is also popular for kids to say when they know a number bigger than their friend (who just proclaimed infinity is the largest number).

Re: Is infinity an odd or even number? (2011)

#363

Post by mulmen »

wpietri wrote: post #352
mulmen wrote: post #332

Earlier quoted context omitted.

Phrases like "you won't always have a calculator at hand" only serve to erode trust in the educator. It's simply not compelling, and for all practical intents and purposes is untrue. Even on backpacking trips I have a cell phone, even if it is off. If you believe mental math is useful then say that and explain the benefits. Students can smell a lie.

That sounds like an excellent thing to somebody who actually said "you won't always have a calculator at hand". Maybe you should find someone like that.

Are we in the same thread?

Re: Is infinity an odd or even number? (2011)

#364

Post by r0uv3n »

chasd00 wrote: post #342

I would say it’s even. If it’s not then the fact that infinity = infinity + 1 means it is :)

In the ordinals infinity != infinity + 1 (but 1 + infinity=infinity). You are right that infinity is even, and in fact infinity+1 is odd. All this is explained in the first answer of TFA.

Re: Is infinity an odd or even number? (2011)

#365

Post by r0uv3n »

remram wrote: post #214
Sharlin wrote: post #81

Earlier quoted context omitted.

There's always someone who sees a question in a submission title and feels the need to comment simply to answer said question in the most boring, banal, and least insightful way possible. Most people realize that if an article that poses a seemingly-simple question makes it to HN frontpage, there's almost certainly some unexpected, interesting, and/or insightful discussion there that reveals that the question wasn't…

I am not preventing the discussion or claiming that you shouldn't extend this concept, just objecting to the way to question is formulated ("is infinity an odd or even number "). The stackexchange comments agree with me, and do this extension by pointing out reasons it would be useful to pick one or the other, but I found it important to point out this caveat that there is no logical answer (in terms of numbers ) and…

Ordinals are often also called ordinal numbers. Both ordinal and cardinal numbers are very much generalisation of natural numbers to a more general concept of number, depending on if you see counting sizes of sets or denoting position (e.g. first, second, etc.) as the fundamental thing numbers do. Of course there are also other notions of number that focus on other aspects (e.g. number fields). But I think it's definitely not wrong to call all of these things numbers.

So it seems weird to me to object to the form of the question, it is perfectly fine as it is. If the question was "is infinity an odd or even natural number?", then of course you'd be right.

All of these things are also stuff one could discuss with a 6 year old (i.e. tell them that there are multiple notions of numbers that focus on different aspects, and that the question has a different (probably interesting) answer in each of these different contexts). Insisting that infinity is not a number seems like a less interesting way to talk about this, without even being necessarily more rigorous.

Edit: See also [0], linked in the second answer

[0]: https://math.stackexchange.com/a/36298

Re: Is infinity an odd or even number? (2011)

#366

Post by r0uv3n »

lo_zamoyski wrote: post #103

It isn't clear to me infinity is a number in the first place. Reification and category mistakes are as much a danger in math as anywhere.

The concept of "number" has a lot of definitions in mathematics. I agree with this [0] more in depth explanation that calling infinity strictly not a number is not useful (though it certainly is not e.g. a natural number). But more importantly, the concept of evenness readily generalizes to ordinals, so as long as we specify that we are in (or move into) that context, then the question is well formed and interesting.

[0]: https://math.stackexchange.com/a/36298

Re: Is infinity an odd or even number? (2011)

#367

Post by ironSkillet »

catiopatio wrote: post #353
ironSkillet wrote: post #346

Earlier quoted context omitted.

Mathematicians consider two sets to be of the same size or more precisely "cardinality", if it is possible to construct a 1-1 map of elements from the first set to the second set. These maps can obviously be constructed for sets with finitely many elements, and they can be constructed for sets with an infinite number of elements as well. For instance, the set of all integers has the same cardinality of the set of all…

> It is in this sense that there are infinities of different sizes. They aren’t actually different sizes, though. All this proves is that under specific set theoretic assumptions , a contradiction arises if you define “size” as “cardinality” and assume that a particular bijective relation exists between your two infinite sets. It doesn’t actually mean the sets have different sizes, it just means they differ under a s…

> They aren’t actually different sizes, though.

What's your precise definition of size that allows someone to actually make a rigorous argument comparing the size of any two sets?

Re: Is infinity an odd or even number? (2011)

#368

Post by cubefox »

mkup wrote: post #164
w0mbat wrote: post #79

Infinity is not a number, it's the absence of a limit.

Absense of limit is not always an infinity, e.g. for sequence (-1)^n. Even if sequence is unbounded, it does not always converge to infinity, e.g. n^((1+(-1)^n)/2): 1, 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, 12, 1, 14, 1, 16, 1, 18, 1, 20 ... Convergence of sequence x(n) to infinity by definition is: for each real number ε>0 there exists a natural number N(ε) such that for every number n≥N(ε) we have |x(n)|>ε.

What would be x in case of the natural numbers?

Re: Is infinity an odd or even number? (2011)

#370

Post by drexlspivey »

paulddraper wrote: post #208
kibwen wrote: post #43

Earlier quoted context omitted.

This just implies that infinity is both even and odd, which means that the statement "infinity is even" is still technically correct by this reasoning.

Odd is defined as not even.

in javascript maybe
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