XKCD: It's more than a comic

It's more of a concept or a direction.

However, once your numbers get transfinite, you could consider the notation as being base-infinity if you squint.

Edited by TParadox on Sep 5th 2018 at 10:47:07 AM

math is stupid and i hate it, is what i'm learning

i guess that's why i'm a psyche major!

Edited by EpicBleye on Sep 5th 2018 at 11:50:19 AM

psh, this guy aint so smart. i can do that

∞1, ∞2, ∞3

easy

He's really pushing it with his "40" joke, isn't he?

I wonder how many mad mathematicians there are. The mad scientist always get all the attention.

As an aside, there is a book, The Outer Limits of Reason by Noson Yanofsky, that deals partly with these number sets, and more in particular, whether or not you could prove them, and what you can and cannot prove mathematically.

Yes, mathematicians have proven that you cannot prove certain theorems.

An "infinity base" system would be, I suppose, one where each natural number is represented by a new, different digit. As with unary, I don't see how reals could be represented in such a system.

For example, represent each number with a line (more precisely line segment) with the length as the value of the number, in some predefined unit. This way you can represent any positive real number (theoretically, at least). Unlike with "traditional" numeric systems, which cannot represent irrational numbers. So no, not all real numbers can be represented like this, for example you cannot write down the exact value of pi, but you can approximate it with arbitrary precision. On the other hand, you can represent any rational number.

Mad mathematicians don't get as much press. After all, there's only so much one can do with a deranged proof or a diabolical formula. Whereas rampaging bioweapons, killer robots, and the like are much more noticeable.

Edited by danime91 on Sep 6th 2018 at 9:15:27 AM

Here's another: The difference between 1 and .9999~ is infinitely small.

The subprime mortgage crisis might beg to differ... although in the mathematician's defense, he told them that that one variable was only assumed to be 1 for convenience sake, and that it needed to be adjusted with further data.

That's more a negligent or evil mathematician, not a mad mathematician.

Yeah, they knew what they were doing, they just didnt care.

Infinitely small is the same thing as saying they're the same. Isn't it proved that nonzero infinitesimals aren't possible? At least in relation to normal numbers.

"Infinitely small" is not a precise mathematical term. If you want to prove this theorem using calculus, then you have to understand what a limit is. The limit of 0.999... is 1 as the number of digits approach infinity. This means that for any, arbitrarily small, but positive, x, there exists a K>0 such that for all k>=K, 0.999...(k) > 1-x. And just to be more precise, by 0.999...(k), I mean this: sum[i=1..k](9/10^i).

Note: I didn't prove the theorem here. I just stated it.

Edited by petersohn on Sep 6th 2018 at 10:55:00 AM

It reminds me of that old logic problem which "proves" that an arrow can never arrive at its target because first it must pass the halfway point, and then the new halfway point, and then the new one, forever, never making it to the original target.

That would be Zeno.

There's a joke based on Zeno's Paradox that I kind of like.

A mathematician and an engineer are both seeing the same woman, and they both have decided they want an exclusive relationship. The woman tells them, "okay, you stand on one side of the room, and I'll be on the other. The first one of you to kiss me is the one I'll stay with. But consider! Before you can get to the other side of the room, you'll have to get halfway across. And then halfway across that." And halfway across that, and so on. The mathematician ponders this and walks away, head low. The engineer strides confidently across the room, kisses her, and says, "close enough to be functional".

The original version is that Achilles and a turtle have a race, and the turtle has a head start. By the time Achilles reaches the point where the turtle started, it will have moved forward somewhat. By the time Achilles reaches that point, the turtle will have moved forward even more. Even though Achilles moves much faster than the turtle, he can never overtake it.

The moral of the story: the ancient Greeks didn't know calculus.

Boathouses and Houseboats

The mathematical resolution to Zeno's paradox, by the way, is that infinite series can have a finite sum; which is to say that 1/2 + 1/4 + 1/8 + 1/16 + ... is equal to exactly one. Which is, as noted, very similar is principle to saying that 0.999999... =1.

Or, perhaps it's easier to look at it the other way: Despite the so-called paradox, the arrow absolutely can hit the target, which is experimental evidence that proves infinite series can have a finite sum; if that's not true, then Math has completely ceased to function as a model for anything in reality.

As a child, I just accepted that one of the other forces, such as gravity, tipped it over into that last bit of the gap. :-P Yes, I know, mathematically naive.

A more philosophical solution to the paradox is that its an artifact of the way we use language to describe the world. Any finite distance is itself divisible to an infinite degree, but that does not imply that there is an infinite distance to cross. The fact that this is confusing to us says more about the limits to human comprehension than it does anything happening in the real world.

One thing to keep in mind too is that those subdivisions of distance are also subdivisions of time. The object still moves at the same speed, it doesn't "slow down with each iteration".

I'm guessing the latest one I posted isn't that interesting, then?