What is the Name of this Math Operation?

...." subscripts are also used frequently in mathematics to define different versions of the same variable: for example, in an equation x₀ and x_f might indicate the initial and final value of x, while v_rocket and v_observer would stand for the velocities of a rocket and an observer. Commonly, variables with a zero in the subscript are referred to as the variable name followed by "nought" (e.g. v₀ would be read, "v-nought").^[3]

Subscripts are often used to refer to members of a mathematical sequence or set or elements of a vector. For example, in the sequence O = (45, −2, 800), O₃ refers to the third member of sequence O, which is 800."...

https://en.wikipedia.org/wiki/Subscript_and_superscript#:~:text=Subscripts%20are%20often%20used%20to,sequence%20O%2C%20which%20is%20800.

https://math.stackexchange.com/questions/123699/what-do-subscripted-numbers-in-an-equation-mean

The subscript I am referring to is on the bottom left of the major number, as written in my first post.

Had an emergency before I could expand my response.

Found a Wiki article that explains different notations of hyperoperations:

https://en.m.wikipedia.org/wiki/Pentation

I cannot copy over the bits I want.

The older I get the more "emergencies" that I have. It is not wise, at a certain point, to drive past porcelain, or even walk past.

Thanks for shining the fog lights on a 70 year old lesson that was occluded by so many birthday parties.

(Eventually had to quit using candles, the heat kept driving me back.)

As the inventor of the boomerang said "It all comes back to me now."

you are right! That is what I was looking for. Thanks.

Easy to see why the numbers become very large very quickly.

^{Easy to see why:}

65536 squared= 4294967296

Largest numbers described in video:

https://youtu.be/u1x_FJZX6Vw

You shook some cobwebs loose… in my college calculus, it was at the suffix.. sub -

an example of 32 ₂ And was called (32 sub 2) but dam… after over 45 years, that’s all I got, I can’t recall how it was applied,,,

First, I think you wrote it wrong, in my opinion it would be 2¹⁰. And the operation would be "exponentiation."

But I have seen the subscript in front of the symbol for indicating nuclides: ₉₂U²³⁵, for the 92nd element, uranium, with a weight of 235 including 92 protons and 143 neutrons.

Here is a video that explains it very simply, and links there explain a lots of other expressions

https://youtu.be/-bCrJiJIFys

Somewhere in that link it refers to numbers "greater than the number of atoms in the observable universe" as if it's impressive. That's about 10⁸⁰, so it's quite easy to come up with a nunber greater than that.

IPV4 has available addresses exceeding that number.

Not with you. According to Wiki

IPv4 uses a 32-bit address space which provides 4,294,967,296 (2³²) unique addresses, but large blocks are reserved for special networking purposes.

You are right.

I should have said IPV6,which is still not enough.

https://www.techtarget.com/whatis/feature/IPv6-addresses-how-many-is-that-in-numbers

Is that the same number as the number of internet and phone scammers in the observable universe?

Gosh, a harder question is "What is it used for?"

Good question.

Don't hold me to this, but from my post I believe it was just used as an identifier.

It’s for getting GA votes within internet discussion fora.

I remember a math instructor telling the class “Today we will discuss fourth and fifth hyperoperations, something most of you will never see or hear of again… unless you become a math teacher.”

For me, this prediction was correct… until yesterday.

something most of you will never see or hear of again. This is the one that applies to me, plus I never heard of it in the first place! Don Knuth was a year or two ahead of me in college, so this notation was developed after I did my education. (Aside: Don was a wonder in college on computer and math, but we were in different fraternities so I didn't hear about him until later in alumni publications.)

Ditto. Before today, I have never heard of or seen this kind of mathematical notation. Can't think of any reason why I would ever need to use it either. I file this under, "Math, for Math's Sake".

Interesting comment in Solar Eagles post #1 "while v_rocket and v_observer would stand for the velocities of a rocket and an observer."
I would have thought that somebody (Observer) watching a Rocket would be standing still so the Velocity would be zero. As the rocket accelerates the velocity would be constantly changing so it would be almost impossible to make any calculation.

It is necessary to know the difference between velocity and speed. Velocity is a vector quantity and includes direction as well as speed.

"I would have thought that somebody (Observer) watching a Rocket would be standing still so the Velocity would be zero."

True if the reference frame is the observer's. If another reference frame is used, it is common to use v_rocket and v_observer, obviouusly refering to speeds relative the arbitrarily chosen inertial reference frame.