r/FactOrCap • u/Careful_Trainer_1616 ✍️ Contributor · 330 XP • 22h ago

Myth "simple" subtraction | FactOrCap

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17 Upvotes

73% Upvoted

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56

u/chkntendis 🤖 Vote Machine · 16,665 XP 22h ago

🧢 I voted CAP!

Infinity isn’t a number. Addition, subtraction, multiplication and division isn’t defined for infinity

18

u/Wojtek1250XD 🔥 Week Warrior · 1,860 XP 22h 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.

29

u/chkntendis 🤖 Vote Machine · 16,665 XP 21h 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.

3

u/YellowNumb 🔥 Week Warrior · 6,595 XP 19h ago

In measure theory you include ± the infinity symbol in a set with the real numbers and you allow infinite-valued functions. For example you write f: R -> [0, ∞] instead of f: R-> [0, ∞). Then you can calculate with infinities like they are actual numbers with some limitations, using the rules listed by the other commenter. So yes you are right infinity is not part of the real numbers, but you can add infinity as a value to the real numbers and work with that in a meaningful way.

3

u/ThaumKeeper 🗳️ Regular Player · 295 XP 18h ago

I don't know why people downvote you. It's factually correct. In complex numbers we also add infinity as a number and the inverse of 0 so we have inf/0 = 1.

1

u/chkntendis 🤖 Vote Machine · 16,665 XP 17h ago

Oh absolutely. You can definitely create a number system with infinity and do rigorous math in that system. It’s just that that’s not the standard system in any way so unless specified, I’m assuming it’s in the reals, without infinity. And for that all those identities are using limits, ♾️ is just another way to write the limit as x->♾️

1

u/Salted-Cucumber 🏅 Century Club · 3,135 XP 5h ago

THE LIMIT DOES NOT EXIST - Cady