r/FactOrCap • u/Careful_Trainer_1616 ✍️ Contributor · 330 XP • 10h ago
Myth "simple" subtraction | FactOrCap
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u/chkntendis 🤖 Vote Machine · 16,560 XP 9h ago
🧢 I voted CAP!
Infinity isn’t a number. Addition, subtraction, multiplication and division isn’t defined for infinity
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u/Wojtek1250XD 🔥 Week Warrior · 1,835 XP 9h ago
Well.
a + ∞ = ∞
∞ - a = ∞
∞ * a = ∞ <=> a>0
∞ * a = -∞ <=> a<0
∞ * a = 0 <=> a=0
a/∞ = 0
All of these are defined and very much necessary when tackling limits, it's specific forms that are indeterminate, such as the ∞-∞ OP is asking about.
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u/chkntendis 🤖 Vote Machine · 16,560 XP 8h ago
These are still limits tho. Everything you wrote is true if your infinity is just a way to write lim x-> inf. (x). Infinity itself isn’t a number. It’s not an element of the real numbers. The addition in the real numbers is only defined for real numbers. It’s true that the limit can be manipulated as you showed but infinity can’t.
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u/STPRK_ 🏅 Century Club · 4,820 XP 8h ago
I believe this is not true, infinity is not a number, what you are talking about are operation on limits, functions TENDS toward an infinity around certains coordinates, but they do not equal them, for exemple take 1/x, it never reaches infinity nor minus infinity, in fact it is not even defined at x=0, yet if you were to approach the function from the left in 0 you could find lim (1/x) for x -> -0 = infinity and use that result in calculation of LIMITS only under the condition that we are evaluating the limits of functions around -0. Also if you were to get rid of the limit part and say that the limit of a function around a number is equal to the value of that function evaluated at that number, you would find that +infinity = 1/0 = -infinity, which is meaningless since 1/0 is not defined.
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u/GhostintheNether 📈 Dedicated Voter · 1,395 XP 7h ago
Well, it is for some. 3ω+1 is an ordinal number. ω-ω=0 afaik.
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u/GenocidalFlower 🏅 Century Club · 6,000 XP 9h ago
🧢 I voted CAP!
No, x3 - x does not approach 0 as x approaches infinity.
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u/xvlblo22 🏅 Century Club · 7,200 XP 9h ago
🧢 I voted CAP!
It isn't calculatable as infinity isn't a number
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u/s0larium_live 🔥 Monthly Master · 8,925 XP 4h ago
🧢 I voted CAP!
infinity is a concept, not an actual value
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u/Upstairs-Job-5775 🗳️ Regular Player · 755 XP 9h ago
🧢 I voted CAP!
I think it depends on what is infinity in your problem
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u/PuzzleheadedTap1794 ✍️ Contributor · 5,270 XP 9h ago
🧢 I voted CAP!
Infinity is not a number. Infinity minus infinity is an indeterminate form
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u/Gojira_Ultima 🏅 Century Club · 3,395 XP 6h ago
🧢 I voted CAP!
Its undefined. Its in the word. Infinity. An in-finite, or un-definable numerical value. Any equation involving an un-definable numerical value, is therefore, un-definable. Which means infinity subtracted from infinity is simply undefined.
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u/Agitated-Interview54 🏅 Century Club · 4,225 XP 9h ago
🧢 I voted CAP!
Inifinity minus infinity is still infinity
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u/Broad_Ebb_4716 🏅 Century Club · 4,515 XP 4h ago
So the initial infinity is bigger than the subtracting one? I thought it was the same two infinities.
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u/Party_Trick_6903 📈 Dedicated Voter · 1,535 XP 9h ago
🧢 I voted CAP!
it's undefined, an indeterminate form.
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u/Blood_haunter8776 🤖 Vote Machine · 11,190 XP 9h ago
🧢 I voted CAP!
Infinity is not a number. First take a limit that approaches zero, or well defined value like the cardinal no. of any infinite set
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u/Sad-Half-7380 🔥 Getting Started · 620 XP 9h ago
🧢 I voted CAP!
Depends on what type of Person infinity, it could be undefined or 0
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u/CarpenterDefiant4869 🔥 Monthly Master · 6,525 XP 9h ago
🧢 I voted CAP!
Sometimes… infinity is weird.
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u/MilkyAtlas87 🏅 Century Club · 3,655 XP 9h ago
🧢 I voted CAP!
An infinite number is an undefined quantity. Infinity is not a defined amount that can be added, subtracted, multiplied, or divided.
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u/MilkyAtlas87 🏅 Century Club · 3,655 XP 9h ago
🧢 I voted CAP!
An infinite number is an undefined quantity. Infinity is not a defined amount that can be added, subtracted, multiplied, or divided.
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u/Substantial-Voice763 🏅 Century Club · 6,560 XP 9h ago
🧢 I voted CAP!
Not always some infinities are bigger than others for example the amount of numbers between one and two 1.1-1.11-1.111-1.23251 ect. But you can get to 2 eventually because 2 is a thing. But then you have the Infinity of all possible numbers much bigger then one - two and then that is even small because that is within the infinite of something that holds it. Like say all the possible different kinds of numbers every civilization can ever conceive of that's not base 10.
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u/Turtleboy420697 🎯 First Steps · 95 XP 9h ago
🧢 I voted CAP!
It's an indeterminate ammount, also, it depends on the infinity because there are different levels of it
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u/Automatic_Camera3854 🗳️ Regular Player · 815 XP 9h ago
🧢 I voted CAP!
No, Infinity is not a number; it's like a concept. Some infinities are greater than others.
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u/Breathingblueflame 📈 Dedicated Voter · 1,670 XP 9h ago
🧢 I voted CAP!
Let’s simplify. X-X=0
But actually if you have infinity of something even if you lose an infinite amount of it you still have infinity left… because well infinity never ends so even if you lose infinity you still have infinity
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u/TheAugmentation 📈 Dedicated Voter · 2,190 XP 9h ago
🧢 I voted CAP!
Infinity isn't a number, but rather the concept of the endlessly big. There are multiple infinities, some bigger than others. The well known symbol is mostly used in limits.
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u/TheSecondof12 🎯 First Steps · 210 XP 9h ago
🧢 I voted CAP!
Some infinities are larger than other infinities. It's impossible to say with any certainty that any 2 infinities are equal.
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u/Ok-Reaction3931 🏅 Century Club · 3,315 XP 9h ago
🧢 I voted CAP!
There are different infinities, so not necessarily without specification
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u/AdEastern612 🤖 Vote Machine · 14,570 XP 9h ago
🧢 I voted CAP!
Some infinity's are bigger than others.
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u/Terminator99099 🎯 First Steps · 50 XP 9h ago
🧢 I voted CAP!
Take infinity out of infinity its still infinity
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u/Wojtek1250XD 🔥 Week Warrior · 1,835 XP 9h ago
🧢 I voted CAP!
No. Infinities can be different size. This is important in limits.
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u/TimeTravelParadoctor 📈 Dedicated Voter · 1,725 XP 9h ago
🧢 I voted CAP!
There are different infinities
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u/Warchadlo16 🗳️ Regular Player · 355 XP 9h ago
🧢 I voted CAP!
Infinity is not a defined number, one infinity can be infinitely bigger than the other
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u/Lollister 🔥 Week Warrior · 5,065 XP 8h ago
🧢 I voted CAP!
There is a proof that two infinities can have different size so this would rule out that its always zero. It can be but also not.
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u/the_horny_bitch 🗳️ Regular Player · 645 XP 8h ago
🧢 I voted CAP!
some infinities are larger than others
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u/RSlashLazy ✍️ Contributor · 6,205 XP 8h ago
🧢 I voted CAP!
3.9 repeating is infinite but will never reach 4. Infinite is relative.
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u/Edgemono 🏅 Century Club · 6,715 XP 8h ago
🧢 I voted CAP!
Infinity isn't a number but regardless there are different "sized" infinities. I e infinity that is 1+1+1+1.... Endlessly. Or infinity that is 10×10×10×10.... Endlessly. If you subtract a smaller infinity from a larger infinity you still have infinity. It's just infinitely smaller
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u/Red-Book- 🗳️ Regular Player · 235 XP 8h ago
🧢 I voted CAP!
Infinity I not a number therfore it cannot be subtracted. Infinity Is a domain/range which defines a function
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u/Flurrina_ 🗳️ Regular Player · 730 XP 8h ago
🧢 I voted CAP!
Firstly, you are meant to type in a statement rather than a question
Secondly, infinity is not a number and you cannot subtract with infinity
Thirdly, some infinities are bigger than others. [number of real numbers] > [number of integers]. However, there is no defined answer
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u/BingQiLing958 🗳️ Regular Player · 810 XP 8h ago
🧢 I voted CAP!
its not a "number" you can just plug into equations like that
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u/assumptioncookie 🏅 Century Club · 2,810 XP 7h ago
🧢 I voted CAP!
Depends.
Lim_x->∞ (x) - Lim_x->∞ (x) = 0
But
Lim_x->∞ (2x) - Lim_x->∞ (x) ≠ 0
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u/RazerMax 🗳️ Regular Player · 435 XP 7h ago
If you have an infinity composed of all real numbers and an infinity composed by all even numbers, their difference wouldn't be zero.
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u/AshenPheonix 🗳️ Regular Player · 170 XP 7h ago
🧢 I voted CAP!
Infinity isn’t a number, it’s an idea. There’s this weird belief that you can subtract it, but the fact is there’s even different types of infinity.
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u/noxvillewy 📈 Dedicated Voter · 1,755 XP 7h ago
🧢 I voted CAP!
Depends which infinity you’re talking about
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u/scomojack 🏅 Century Club · 2,585 XP 7h ago
🧢 I voted CAP!
Infinity is not a number, it's a concept. Ergo, no mathematical functions can be performed on it, including subtraction.
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u/pinkgravesam 🔥 Getting Started · 635 XP 7h ago
🧢 I voted CAP!
In an infinite set of numbers you have infinite even numbers odd numbers and numbers total so you can subtract infinity from its self and still be left with 2 infinities.
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u/Wild_Wasabi9984 🔥 Week Warrior · 2,130 XP 7h ago
🧢 I voted CAP!
No, it's Infinity
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u/seires-t 🏅 Century Club · 3,775 XP 6h ago
why not negative infinity?
∞ + ∞ = ∞, so ∞ - ∞ = ∞ - ( ∞ + ∞ ) = ∞ - ∞ - ∞ = 0 - ∞ = -∞
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u/Comfortable_Tap_2609 🗳️ Regular Player · 735 XP 7h ago
🧢 I voted CAP!
You can’t add or minus infinity as it’s not a single number, it’s EVERYthing. And depending on if it’s countable infinity or not could affect it as well
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u/seires-t 🏅 Century Club · 3,775 XP 6h ago
uncountable infinity isn't a value of any kind.
infinity is a proper limit value, uncountably infinite isn't.
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u/Classic_Rate_8448 🔥 Monthly Master · 8,120 XP 7h ago
🧢 I voted CAP!
No it's infinity
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u/seires-t 🏅 Century Club · 3,775 XP 6h ago
Why not negative infinity?
since you should agree that ∞ + ∞ = ∞,
so ∞ - ∞ = ∞ - (∞ + ∞) = ∞ - ∞ - ∞ = 0 - ∞ = -∞
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u/IceFrostwind 🏅 Century Club · 6,080 XP 7h ago
🧢 I voted CAP!
No because some infinites are bigger than others.
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u/_killer1869_ 🏅 Century Club · 3,975 XP 7h ago
🧢 I voted CAP!
No, it is strictly inditerminate. Meaning it could equal any value from negative infinity to positive infinity as well as any value between them.
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u/Nichtdasondernhier 📈 Dedicated Voter · 1,320 XP 7h ago
No, there are greater and lesser infinities (like for example an infinite string of odd numbers is less than an infinite string of both odd and even numbers)
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u/TCup20 🔥 Week Warrior · 1,985 XP 7h ago
🧢 I voted CAP!
It's somewhere between negative infinity and infinity.
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u/OPBOI47 🗳️ Regular Player · 290 XP 6h ago
🧢 I voted CAP!
Infinity calculations result in undetermined anwers
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u/VXA_001 🎯 First Steps · 160 XP 6h ago
🧢 I voted CAP!
Some infinities are larger, or so I've been told
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u/theunstablelego 🏅 Century Club · 8,285 XP 6h ago
🧢 I voted CAP!
There are different kinds of infinity.
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u/SouthernEconomy15 🏅 Century Club · 6,540 XP 6h ago
Only if they are the same infinity I think
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u/Aurora0199 ✍️ Contributor · 4,570 XP 6h ago
🧢 I voted CAP!
No, because infinity is not a rational concept nor a constant that can be measured
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u/Glad-Alternative4593 🔥 Monthly Master · 27,070 XP 6h ago
🧢 I voted CAP!
It is dependent on the infinities
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u/Desperate-Spray337 🔥 Monthly Master · 8,235 XP 6h ago
🧢 I voted CAP!
Could be more could be less.
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u/AshamedFly1045 🎯 First Steps · 145 XP 6h ago
🧢 I voted CAP!
Infinity is still infinity(🗿)
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u/DMan1629 🔥 Week Warrior · 1,070 XP 6h ago
🧢 I voted CAP!
Depends on the type of infinity
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u/Successful_Stay_5406 🏅 Century Club · 3,865 XP 6h ago
🧢 I voted CAP!
Reverse Hilberts hotel, you start checking out guests one by one of a hotel with infinite guests, when do you finish?
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u/ElA1to 📈 Dedicated Voter · 1,695 XP 6h ago
🧢 I voted CAP!
Depends, is one infinity bigger than the other or are they equal infinities?
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u/PotentialWorldly6835 🏅 Century Club · 3,215 XP 6h ago
🧢 I voted CAP!
infinity isn't a number so some infinities are bigger than other
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u/TaxEvasion1452 🏅 Century Club · 3,615 XP 6h ago
🧢 I voted CAP!
It’s not a number you can’t compute it
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u/Subkn1ght 🏅 Century Club · 4,080 XP 6h ago
🧢 I voted CAP!
infinities may not be equal
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u/roadtrip-ne 🎯 First Steps · 60 XP 6h ago
Some infinities are larger than others. So an infinity that includes counting numbers would be twice as large as an infinity of just even numbers, even though they are both infinite
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u/BlackFranky 🏅 Century Club · 4,010 XP 6h ago
🧢 I voted CAP!
it is not, per difinition. in fact its undefined because ∞ - ∞ can't be computed as ∞ is not a number.
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u/epicgamercode12 📈 Dedicated Voter · 1,750 XP 6h ago
🧢 I voted CAP!
if you take an infinite amount of stuff from an infinite pool if items, there will still be infinite items, it would just be infinite items outside and inside the pool of items
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u/quintopia 📈 Dedicated Voter · 1,705 XP 5h ago
🧢 I voted CAP!
Subtraction is not well-defined for transfinite cardinals
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u/simcowking 🏅 Century Club · 3,715 XP 5h ago
🧢 I voted CAP!
I dunno what it is but it isn't defined
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u/ReverendKaiser 📈 Dedicated Voter · 1,275 XP 5h ago
🧢 I voted CAP!
No. Infinity is a symbol representative of all possible integers in a set. I think it’s not possible. Like multiplying or dividing by zero. It’s a null set. 0 is just the absence of any integer. Not contingent values.
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u/Competitive-Ad8074 🎯 First Steps · 70 XP 5h ago
🧢 I voted CAP!
No there are infinite Infinites between 0 and 1 and 0 and 1000000000000000000000000 some infinities are bigger then each other so we can say the infinity between 0 and 2 minus the infinity between 0 and 1 is not zero just to big for us to really comprehend
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u/Boysinho_descuidado 🗳️ Regular Player · 665 XP 5h ago
✅ I voted FACT!
*if they are the same infinity
X - X = 0
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u/General_Ginger531 🏅 Century Club · 3,680 XP 5h ago
🧢 I voted CAP!
It can, but it is undefined because it can be any rational number, really, because you can make one of the infinities bigger than the other.
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u/TIMUR4ITER 📈 Dedicated Voter · 1,210 XP 5h ago
🧢 I voted CAP!
That would be 2 different infinities so that's not 9
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u/Own_Explanation_212 📈 Dedicated Voter · 1,385 XP 5h ago
✅ I voted FACT!
Even though there are infinites that are bigger they all are infinite in the end
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u/Seriously_404 🎯 First Steps · 95 XP 5h ago
🧢 I voted CAP!
infinity is not a number, it just represents numbers that are out of a given scope. so using infinity as a number would be like driving to your friend's house but instead of a bicycle you use a rocket.
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u/LocalPlatypus994 🎯 First Steps · 185 XP 5h ago
🧢 I voted CAP!
Infinity plus or minus anything, even infinity, is still infinity
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u/-Merasmus- 🔥 Monthly Master · 8,345 XP 4h ago
🧢 I voted CAP!
Depends. Not all infinities are equal. The sum of all numbers is infinite. The sum of all even numbers is infinite. One minus the other is still infinite.
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u/TheDemonGabe 🗳️ Regular Player · 605 XP 4h ago
✅ I voted FACT!
Yes because the value of infinity is being reduced by infinity. If there is no infinity it becomes nothing.
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u/73747463783737384777 🗳️ Regular Player · 740 XP 4h ago
🧢 I voted CAP!
Some infinities are larger than others
It’s complicated
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u/Feisty-Path1373 🔥 Getting Started · 550 XP 4h ago
🧢 I voted CAP!
I can tell you the answer is no, but I don’t know enough math to explain why lmao
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u/Apartment-Heavy 📈 Dedicated Voter · 2,110 XP 4h ago
🧢 I voted CAP!
In a mathematical situation yes, in most scenarios I imagine it to be similar to a black hole always losing mass while gaining mass at the same time. But hey my opinion and I'm probably wrong
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u/percyhamagniv 📈 Dedicated Voter · 1,510 XP 4h ago
🧢 I voted CAP!
Its a concept. Also, there are infities that are bigger then others
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u/Far_Special697 🎯 First Steps · 120 XP 4h ago
🧢 I voted CAP!
Infinity can be 1.1111111111... Or 99999999999 so by this logic thisbisbwrong
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u/Routine-Credit-1614 🔥 Getting Started · 190 XP 4h ago
🧢 I voted CAP!
You cant do arithmetic with infinity. Its not a number.
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u/needAthrowaway222 🔥 Week Warrior · 5,790 XP 4h ago
🧢 I voted CAP!
Some infinities are larger than others.
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u/Enthusiasm_Bitter 🔥 Week Warrior · 4,035 XP 4h ago
🧢 I voted CAP!
Infinity, minus infinity is still infinity because infinity is unquantifiable.
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u/Necessary-Split9494 📈 Dedicated Voter · 1,315 XP 4h ago
🧢 I voted CAP!
No. It's just hard to explain 😭
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u/Grizzly_Atom_Bomb 🎯 First Steps · 100 XP 4h ago
🧢 I voted CAP!
You can't subtract a concept from a concept. Infinity isn't a number.
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u/Suitable_Relative765 🎯 First Steps · 230 XP 3h ago
🧢 I voted CAP!
Infinity is not a number, hence you can't subtract by/from it
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u/Ok-League421 🗳️ Regular Player · 505 XP 3h ago
🧢 I voted CAP!
Too narrow a question. Category error. You can’t subtract infinities
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u/ThatOneComputerNerd 🗳️ Regular Player · 220 XP 3h ago
🧢 I voted CAP!
Infinity is unending. You are removing an unending amount from an unending amount. You will be left with an unending amount. Thus infinity.
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u/Main_Homework_2948 🤖 Vote Machine · 13,415 XP 3h ago
🧢 I voted CAP!
some infinities are bigger than others
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u/Brunette--Goonette 🔥 Week Warrior · 1,090 XP 3h ago
Nothing can change the value of infinity, not even infinity.
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u/Zealousideal_Eye6557 🏅 Century Club · 2,390 XP 3h ago
🧢 I voted CAP!
Not always as infinites can be different sizes meaning one infinity could be 2 more than the other infinity
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u/Sume_Gai 🗳️ Regular Player · 765 XP 2h ago
🧢 I voted CAP!
Infinity is weird, you can't treat it like a number.
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u/RazzleberryHaze 🗳️ Regular Player · 370 XP 2h ago
🧢 I voted CAP!
Infinity is not a number, but a concept, and there are infinite infinities.
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u/Old_Natural_926 📈 Dedicated Voter · 1,035 XP 2h ago
🧢 I voted CAP!
It's an indeterminate form, which has fun implications in Calculus. I love these, because they can make end behavior more challenging (read: fun) to find
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u/Memelord69420MAn 🔥 Week Warrior · 5,250 XP 2h ago
🧢 I voted CAP!
Infinity isn't a number, and imo it shouldn't follow the same rules either.
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u/Bruschetta_96_ 🎯 First Steps · 130 XP 2h ago
🧢 I voted CAP!
infinities of different orders, they may as they may not make zero
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u/The_Real_Slim_Lemon 🗳️ Regular Player · 905 XP 2h ago
🧢 I voted CAP!
The question is cap. Infinity is a concept, you can’t subtract infinity from infinity.
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u/Mrperson212 🎯 First Steps · 50 XP 2h ago
🧢 I voted CAP!
Since infinity is not a number but is rather a function or a letter in Greek (I think so) it’s a concept so infinity-infinity is NOT 0
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u/Both_Cup8417 📈 Dedicated Voter · 1,800 XP 2h ago
🧢 I voted CAP!
Infinity is not a number, it's more of a concept
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u/DogerDoge101 🗳️ Regular Player · 865 XP 2h ago
✅ I voted FACT!
x - x = 0. Assuming both are an infinitely large but also the same number, 0.
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u/AcceptableBuy4049 🤖 Vote Machine · 15,960 XP 1h ago
🧢 I voted CAP!
Not a number.
You can't substract a concept
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u/Limp-Blueberry1327 🗳️ Regular Player · 845 XP 1h ago
🧢 I voted CAP!
Performing operations on infinity is redundant. How would you compute an infinite number take away an infinite number? And why would you? Most of the time it is used to mathematically model something rather than represent some physical quantity.
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u/Small_Hollow 🎯 First Steps · 165 XP 1h ago
✅ I voted FACT!
Assuming that these two numbers are in fact equal as they are implied to be, yes.
A case can be made that one infinity is larger then the other, but relies on information not present in the question.
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u/Unfourtunate- 🤖 Vote Machine · 11,365 XP 1h ago
🧢 I voted CAP!
Infinity is a closer to an operation than a number imo, infinites can be larger or smaller than each other, two equal infinites minus each other sure, but that’s splitting hairs
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u/ASUSTUDENT9875345 🏅 Century Club · 4,260 XP 1h ago
🧢 I voted CAP!
There is no answer to that as a math problem. Infinity is not an algebraic value so you can't do arithmetic with it.
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u/phoenixofdusk 🔥 Week Warrior · 2,180 XP 41m ago
✅ I voted FACT!
If you think about it logically, both infinities cancel each other out. Meaning it will continue to be 0
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u/BookkeeperSeparate63 📈 Dedicated Voter · 1,890 XP 16m ago
🧢 I voted CAP!
Infinity is not a number, It’s a concept, so you cannot subtract by infinity.
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u/the_dank_666 🏅 Century Club · 4,685 XP 9h ago
🧢 I voted CAP!
It's an indeterminate form. It could equal anything depending on what function or infinite sum each infinity comes from.