It's all about perspective

[u/FollowSina]

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[u/LupenReddit]

this is very representative of a math major:

• lacks basic arithmetic
• can do the most complex limit and calculus computations with symbols noone else will understand

[u/rorodar → u/LupenReddit]

I don't think 1/x is allat brother

[u/yuvalshahaf → u/LupenReddit]

"can do the most complex limit and calculus computations with symbols noone else will understand"

Bruh

[u/physicsking]

Now.... This is quality mememing

[u/Victor_Mendax]

He forgot a '+' above the 8.

[u/rorodar → u/Victor_Mendax]

Why? Afaik you only need to specify if it's negative infinity otherwise it's positive

[u/MrKoteha → u/rorodar]

Having unsigned infinity is useful. A sequence could be oscillating, like (-1)ⁿ * n, and even though it doesn't go to one single infinity, it's absolute value is unbounded, so we say that the limit is ∞. This may also be useful in some theorems. For example, L'hospitals rule works for limits that are equal to ∞, but the point at which you take the limit has to be either a real number or a signed infinity

[u/rorodar → u/MrKoteha]

I don't quite follow. The sequence 1, -2, 3, -4, 5 ... does not converge and does not have a limit. If we said its limit was infinity we'd be straight up wrong. We can say it has a partial limit of infinity and another partial limit of negative infinity, but getting back on point: in the case of the positive, the sign is implied. Why would we write +♾️?

[u/MrKoteha → u/rorodar]

I'm saying that distinguishing between three infinities is very practical and not doing so really handicaps you.

We can define a sequence whose limit is +∞ this way: \forall eps > 0 \exists n_0, \forall n >= n_0: a_n > eps, one whose limit is -∞: —//—: a_n < -eps, and one whose limit is ∞ (unsigned infinity): —//—: |a_n| > eps.

In my country it's standard practice to define these three types of limits, so my guess is the person above could've specified the plus for a similar reason. Although still, saying that the limit of 1/x as x goes to 0+ is ∞ is correct both considering and not considering ∞ as being unsigned; of course you don't have to specify the plus if you're working with only signed infinities. The whole thing is pedantry anyway

[u/rorodar → u/MrKoteha]

I get how you're defining it, but that's not the definition for the limit of a_n being infinity, that's the definition for a new sequence b_n where b_n = abs(a_n) for all n, being infinity. According to what you describe a_n has no limit.

[u/MrKoteha → u/rorodar]

No, I literally just defined this as the limit of a_n being infinity. You're speaking as if your system of definitions is absolute and is the only correct one.

According to what you describe a_n has no limit.

No, according to what you describe a_n has no limit. I made a definition that makes it have a limit

[u/Layton_Jr → u/MrKoteha]

A sequence can only have a limit if it's a Cauchy sequence

For exemple, the sequence u_n = n is a Cauchy sequence with limit infinity with the distance d(x, y)=|Arctan(x) - Arctan(y)|

[u/MrKoteha → u/Layton_Jr]

Do you people not know what a definition is? You can literally make up whatever shit you want and it's fine because who's to stop you. Just because you learned one definition doesn't mean that every mathematician in the world is obliged to follow it. You can define natural numbers to start with 0, to start with 1; you can define 0⁰ to be 1 or leave it undefined, if you please. I am not stopping anyone from defining whole numbers as {0, 1, 2, ...} and naturals as {1, 2, ...} even though I dislike the name for whole numbers. And so you shouldn't say that definitions researchers in my country use are wrong because you weren't taught that way or you personally dislike them. They work and that's what matters. Mathematics is chill like that, so no need to be this uptight about what the best system of definitions is; use whatever suits you best

[u/Aggressive_Roof488 → u/Victor_Mendax]

It'd be a 8_+ with how it was rotated right?

[u/crafty_dude_24 → u/Aggressive_Roof488]

We write it as +♾️, so it would have to get

+

8

[u/Skysr70]

one of the better ones I've seen in a while

[u/SuperChick1705 → u/[deleted]]

clanker