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/sci/ - Science & Math

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5803366 No.5803366 [Reply] [Original]

will infinity + infinity have the same value as infinity * infinity?

>> No.5803369

Fuck /sci/

>> No.5803370

Yes, both are infinity.

>> No.5803377

>>5803370
that is what I was thinking, there is a commercial with this guy talking to a group of kids and he says "sorry we were looking for infinity plus infinity" and then a kid says "what about infinity times infinity" but the I was thinking, wouldn't they both infinity regardless?

>> No.5803381

>>5803377
http://en.wikipedia.org/wiki/Extended_reals#Arithmetic_operations

>> No.5803400

Infinity is a concept, not a number, and as a result cannot be subjected to the same basic arithmetic operations that numbers are subject to.

>> No.5803405

>>5803400
http://en.wikipedia.org/wiki/Extended_reals#Arithmetic_operations

>> No.5803708

>>5803400
lol. It's a transcendental number you idiot

>> No.5805039

Learn set theory. Georg Cantor proved that there are infinite many "degrees'' of infinity.

>> No.5805123

>What is Continuum hypothesis

It's like none of you ever took set theory.

>> No.5805130

>>5805123
Please explain why you think OP's question requires knowledge of the continuum hypothesis. I could need a good laugh at how you misunderstood CH.

>> No.5805166

>>5803400
Unless you define it. Because that's how math works.

>> No.5805197

Typical thread on /sci/: Everyone pretends to know the answer and no-one is willing to explain anything.

I just happened to look up cardinality on wiki and happened upon cardinal arithmetic. So you can perform arithmetic operations on infinities it seems.

>> No.5805292

>>5805197
When thinking about sets, the cardinality of the cross produkt of two sets is the same as the product of the cardinalities of the sets.
| M x N | = | M | * | N |
The cross product of two infinite sets will have the cardinality of the set with the higher cardinality.
If two sets are disjoint, then
| M u N | = | M | + | N |
The union of two infinite sets will have the cardinality of the set with the higher cardinality.

so in this sense infinity+infinity has the same value as infinity*infinity.
I might also add, that 2^infinity > infinity in this sense, since cantor proved that the power set of a set has allways a higher cardinality

>> No.5805295

>>5805197

I will

the rational plane can be thought of as infinity times infinity

it is countably infinite

short answer: yes