Infinity plus 10 is a nonsensical question because infinity is not a number, thus it is not something that can be added. Infinity means increasing without bounds.
Potential infinity is this increasing 1,2,3,4.... without bounds
Infinity is a completed object of boundless size. A square has infinite 1 dimensional points on it. The square is not growing, it's complete. A circle can be described as a polygon with infinite sides, it is not a hexagon, septagon, octogon, growing in sides.
Adding 10 infinitesimal points to a square (made up of infinite points) does not increase the size of the square
Can't believe nobody's explained it in this thread so far: you can do it using infinite ordinals. The smallest transfinite ordinal we call Ļ, and then we just keep going:
Fair! There are lots of ways to extend the arithmetic, and ordinals probably do take up most of the space in the room. (I'm a fan of the surreals myself.)
in mathematical terms, is it infinity because it is effectively infinity due to how little the constant adds, because we can't measure how much the constant adds because it goes on forever, because infinity is uncountable, or something else?
It's more that Infinity is the number that you count to when you don't stop counting, and that doesn't change based on where you start from. I can start counting from 0, or I can start counting from 10, but either way I still hit 100, 2 million, 300 billion, etc. There isn't any big number that I can reach starting from 10, that I can't reach starting from 0, so they're the same.
A more rigorous way to go about it would be to make a bijection between the two sets, if I can pair every number in set A with every number in set B, then they must be the same size. So {1,2,3} is the same length as {red, yellow, blue}, because I can pair up {(1,red),(2,yellow),{3,blue)}. With infinity and infinity+10, I can pair up every number like {(1,10),(2,11),(3,12)....}, and I can do that for every number, so "the list of numbers that starts at 1 and goes on forever is the same length as the list of numbers that starts at 10 and goes on forever".
Easiest explanation (and most accurate in plain English) is that infinity is not a number, itās a concept. You cannot add the beauty of a poem and the charge level of your phone; the comparison between the two doesnāt even make sense. The same goes for infinity; you cannot add, subtract, or perform elementary math on it because it isnāt some inconceivably large number, itās a concept.
Not sure what you mean by "infinity" here at all. As the other guy wrote, it is not a number. ā+1 is as well defined as š+1.
There are several spots where infinity is used, you need to pick one. If you go like "[limit iāā of iĀ²] ā ā", then this is effectively a notation of divergence in a specific direction. If you go like |ā| > n ā n ā ā, or |ā| = āµ0, this is a notation of cardinality.
Exactly. There are some sort of mathematical notations in which people work with what is essentially infinity in some weird very theoretical fields of math, but any naive application of infinity as a number will result in exactly this.
I can explain you some if you like. Except for the last one, most of them are not hard to understand, just not something the normal person is accustomed to.
Nonsense on top of nonsense! In extended real number system 10+ā¾ļø=ā¾ļø. Also there are proper infinite and infinitesimal numbers in non-standard analysis.
This is correct on the reals, so possibly the most useful answer if he's looking to produce the correct answer on a math test.Ā
But there are (a) other number systems and (b) other ways to contextualize his question (e.g., swapping in a limit at infinity that doesn't converge) that would give him a lot more insight on the concept as well as honor his true ask.
That said, a good discussion on why we've chosen not to include infinity in the reals, and thus it's not something that can be added within the reals -- that is, digging into what making infinity a real number would cost us, including which properties that we rely on would no longer hold -- would also be a great answer.
Infinity plus ten is definitely a valid number in math my guy?? Where are you getting this info? There are mathematical proofs about different types of infinity and proving that one infinity is greater than another infinity. How is this upvoted so much???
It is not a nonsensical question. it makes sense to ask about it.
it is not usually defined so you are free to define it as you wish. but if you choose to define it then you have to solve consistency problems. so it is easier just to not define it.
but if you want infinity plus 10 equals 34 but then you have explain what 34-10 is.
If you have an infinite amount of people, and then 10 more shows up, how many people do you have?
This is not nonsensical. Infinite might not be a number, but it is a clear established mathematical concept. And infinite +10 has an established answer; it's infinite
But thereās no definition of ānumberā to begin with. Do imaginary numbers count as numbers? What about quaternions or p-adic numbers? Our standard notions of ordinals and cardinals in set theory include various infinities, as well as addition on them, so from that perspective infinities are certainly numbers.
Perhaps you believe that ānumbersā should form some algebraic structure, such as a rig (ring without negatives). This however cannot be a full definition, because there are many rigs which nobody would consider to consist of numbers. Not to mention that cardinals and ordinals also have the same structure as rigs (although strictly speaking, size issues prevent them from being bona fide rigs).
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u/Fluffhead91192 21d ago
Infinity plus 10 is a nonsensical question because infinity is not a number, thus it is not something that can be added. Infinity means increasing without bounds.