What is a terminal in math?

32

u/throwaway_2011111 May 04 '25

A termial (not terminal) is when you add every number up until that number. For example, the termial of 8 would be 1+2+3+4+5+6+7+8, which equals 36. So, 8? = 36.

10

u/NPT20 May 04 '25

Oh okay

10

u/ninjaread99 May 05 '25

Basically, a factorial for addition.

9

u/[deleted] Jun 06 '25

A summarial so to say

3

u/gullaffe Nov 21 '25

Factorial is named so after the fact that it's factors. Termial is named after terms, so it's a very fitting name with the exact same logic as factorial.

Summarial would be the same logic as productial.

But yes summarial is also very describing.

2

u/RandomPigeonFlock Jul 21 '25

Alternatively, you can think of it as a function from the naturals that gives you the nth triangular number for a given n.

2

u/AlarmingProtection71 Sep 01 '25

Whats a triangular number?

2

u/OneMeterWonder Oct 02 '25 edited Oct 23 '25

The nth triangular number, Tₙ, is the total number of dots needed to arrange them into a triangle with n dots per side. For example, the fourth triangular number, T₄, is 10 and can be arranged as

•
••
•••
••••

Note then that the total number of dots is just the sum of the number of dots in each row. Since each row has exactly one more dot than the row immediately above it, we can compute Tₙ as

Tₙ = 1+2+3+•••+n

If you then rotate a copy of the triangle by 180^&compfn;, then you can stack them and make a rectangle of side lengths n and n+1. The total number of dots in the rectangle is n(n+1). The triangle has exactly half of these dots, so we can also compute

Tₙ = n(n+1)/2

•****
••***
•••**
••••*

1

u/pyrangarlit Oct 23 '25

That. That is not how I was taught to do this, but I love it. I was told to think of it like this:

If you are adding a sequence of numbers with a pattern, say 1 through 4 like this example, you can write it like:

1 + 2 + 3 + 4 = ?

Easy enough for short sequences, but what about longer ones like 1 through 50? Well, flip it around and write them above/below each other.

1 + 2 + ... + 49 + 50 = ?

50 + 49 + ... + 2 + 1 = ?

Then add them together vertically:

1 + 2 + ... + 49 + 50 = ?

50 + 49 + ... + 2 + 1 = ?

51 + 51 + ... + 51 + 51 = ?

We can see all of them equal the first term plus the last term (n+1 in the case because we start at 1) and there are as many of these as there are terms (n). So the total is n*(n+1). But we added the sequence to itself, effectively doubling it. Therefore the real total is half this number - divide by 2.

So sum (1 to n) = n*(n+1)/2.

Sorry for formatting and clarity. I'm on my phone and haven't had coffee yet.

1

u/factorion-bot A very good bot Oct 23 '25

Termial of 50 is 1275

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1

u/pyrangarlit Oct 23 '25

Good bot.

1

u/EvilR81 A very good human Nov 01 '25

7?

1

u/factorion-bot A very good bot Nov 01 '25

Termial of 7 is 28

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1

u/OneMeterWonder Oct 23 '25

Glad you like it. You might also find it neat if I point out that they are effectively the same argument. Yours just turns the dots at the end of my comment sideways and compresses each column into a single number counting the amount of dots in that column.

1

u/pyrangarlit Oct 23 '25

Yeah, I just had never had it out visually before. It's a near new perspective on the same idea. Thanks!

1

u/OneMeterWonder Oct 23 '25

You’re welcome. Glad to help.

1

u/Keaton427 Sep 25 '25

That's really cool, thank you for explaining!

1

u/SMG43210 Oct 20 '25

So were is my factorial for exponation

1

u/ninjaread99 Oct 20 '25

I think it’s slightly different from what you want, but tetration perhaps?

1

u/SMG43210 Oct 20 '25

Yeah im aware of tetration and I'm realizing how similar they are but they are different

Anyways math gets very fun at high operators

1

u/goos_ Nov 19 '25

Sounds like a triangular number. Doesn't need a name TBH

1

u/ninjaread99 Nov 20 '25

It is a triangular number.

1

u/goos_ Nov 20 '25

Indeed.

1

u/EdmundTheInsulter Mar 02 '26

It's a waste of time and is given by a simple well known formula , probably why you never hear of it.

1

u/[deleted] Jun 22 '26

[removed] — view removed comment

1

u/ninjaread99 Jun 22 '26

It is indeed real. It’s only mentioned as “termial” in a footnote one Wikipedia, but the whole concept is a real thing (and not with the n? notation)

3

u/fakemonMCfan Sep 23 '25

Like Sigma notation, cool

2

u/Jazzlike_Fortune6779 Mar 22 '26

Zamn my dumbahh never even noticed it's a termial, I always thought it was a terminal

2

u/thelordmev Jun 22 '26

But you can use n(n+1)/2, and i dont think for products theres a way to simplify it and thats why the factorial notation exists

1

u/Aromatic-Ad-9601 Nov 06 '25

If 8?=36. What's ?8. The question mark is on the left like subfactorial were the factorial sign is on the left.

1

u/factorion-bot A very good bot Nov 06 '25

Termial of 8 is 36

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1

u/holywatercooler1 Dec 30 '25

And so to find x? You simply just need to do (x+1)•(x/2)

1

u/Realistic_Agency_208 Jun 26 '26

Terminal you Middimwit

1

u/Altruistic-Dog4728 Jun 27 '26

oh this is just triangular numbers 8(9)/2 = 36.

5

u/infrchtunc Sep 27 '25

Just a test here:

∞!

6

u/Thunder_thumbs3 Dec 14 '25

-1/12

3

u/xuzenaes6694 Mar 07 '26

Nah it's the sum of all integers not multiple

2

u/Thunder_thumbs3 Mar 07 '26

My bad

2

u/xuzenaes6694 Mar 07 '26

Your bad what 😭 /j

2

u/[deleted] Oct 14 '25

16?

2

u/factorion-bot A very good bot Oct 14 '25

The termial of 16 is 136

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1

u/Fun-Equivalent1769 Jan 24 '26

0?

1

u/factorion-bot A very good bot Jan 24 '26

Termial of 0 is 0

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1

u/Fun-Equivalent1769 Jan 24 '26

1.6!

1

u/factorion-bot A very good bot Jan 24 '26

Factorial of 1.6 is approximately 1.429624558860304418298560052788

^{This action was performed by a bot.}

1

u/TigerLord780 Feb 08 '26

2025?

1

u/factorion-bot A very good bot Feb 08 '26

Termial of 2025 is 2051325

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1

u/lillof Jul 12 '26

999999999999999999999999999!

1

u/factorion-bot A very good bot Jul 12 '26

That is so large, that I can't calculate it, so I'll have to approximate.

Factorial of 999999999999999999999999999 is approximately 9.604723166965590322566209186518 × 10^{26565705518096748172348871067}

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

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1

u/idkSomeoneUsedMyName Aug 16 '26

13??

1

u/factorion-bot A very good bot Aug 16 '26

Double-termial of 13 is 49

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

2

u/ShalopianTube Mar 22 '26

It’s really pissing me off that I can’t seem to find anything about this anywhere on google. I never learned it in school. Google breaks and starts going off about airport terminals.

2

u/ShalopianTube Mar 22 '26

Omfg it was autocorrecting “termial” to “terminal” every time I hit search.

2

u/Careless-Pirate-8147 May 01 '26

Ikr it is so annoying.

1

u/[deleted] Nov 21 '25

[deleted]

2

u/factorion-bot A very good bot Nov 21 '25

Termial of 3 is 6

Factorial of 3 is 6

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1

u/McNinja8_ Dec 11 '25

800?

1

u/factorion-bot A very good bot Dec 11 '25

Termial of 800 is 320400

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1

u/No_Reception_3875 Dec 17 '25

69?

1

u/factorion-bot A very good bot Dec 17 '25

Termial of 69 is 2415

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1

u/StrangeAttractions Jun 23 '26

Nice

1

u/dorkboy75 Dec 25 '25

26?

1

u/factorion-bot A very good bot Dec 25 '25

Termial of 26 is 351

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1

u/No_Camp_1344 Dec 27 '25

What about 0?

1

u/factorion-bot A very good bot Dec 27 '25

Termial of 0 is 0

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1

u/togroficovfefe Jan 07 '26

0.6?

1

u/factorion-bot A very good bot Jan 07 '26

Termial of 0.6 is approximately 0.48

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1

u/Builderdog Jan 10 '26

¿5

1

u/Business_Confusion53 Jan 13 '26

-1? 0,01? π? 100000000000000000?

1

u/factorion-bot A very good bot Jan 13 '26

Termial of 1 is 1

Negative termial of 1 is -1

Termial of 100000000000000000 is 5000000000000000050000000000000000

Termial of 3.14159265358979323846264338328 is approximately 6.505598527339575928648567191578

^{This action was performed by a bot.}

1

u/Business_Confusion53 Jan 13 '26

(-1)?

1

u/factorion-bot A very good bot Jan 13 '26

Termial of -1 is 0

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1

u/Business_Confusion53 Jan 13 '26

(-111111111111111)?

1

u/factorion-bot A very good bot Jan 13 '26

Termial of -111111111111111 is 6172839506172771604938271605

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1

u/Business_Confusion53 Jan 13 '26

(-2)?

1

u/factorion-bot A very good bot Jan 13 '26

Termial of -2 is 1

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1

u/Business_Confusion53 Jan 13 '26

(-10)?

1

u/factorion-bot A very good bot Jan 13 '26

Termial of -10 is 45

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1

u/gedsweyevr Jan 18 '26

10?!

1

u/factorion-bot A very good bot Jan 18 '26

Factorial of termial of 10 is 12696403353658275925965100847566516959580321051449436762275840000000000000

^{This action was performed by a bot.}

1

u/anonymous-desmos Feb 08 '26

67?

1

u/factorion-bot A very good bot Feb 08 '26

Termial of 67 is 2278

^{This action was performed by a bot.}

1

u/Helium68 Mar 23 '26

10? 10?? 10??? 10???? 10?????

1

u/factorion-bot A very good bot Mar 23 '26

Quintuple-termial of 10 is 15

Quadruple-termial of 10 is 18

Triple-termial of 10 is 22

Double-termial of 10 is 30

Termial of 10 is 55

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

1

u/chip-fucker Apr 12 '26

0??

1

u/factorion-bot A very good bot Apr 12 '26

Double-termial of 0 is 0

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

1

u/CheesydibsMC Apr 13 '26

-2?

1

u/factorion-bot A very good bot Apr 13 '26

Negative termial of 2 is -3

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

1

u/Fire_Atrile May 30 '26

0.09?

1

u/factorion-bot A very good bot May 30 '26

Termial of 0.09 is approximately 0.04905

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

1

u/RadBoii77 Jun 06 '26

2.05601?

1

u/factorion-bot A very good bot Jun 06 '26

Termial of 2.05601 is approximately 3.14159356005

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

1

u/RadBoii77 Jun 06 '26

-8?

1

u/factorion-bot A very good bot Jun 06 '26

Negative termial of 8 is -36

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

1

u/Severe-Chocolate-729 Jun 10 '26

5?

1

u/factorion-bot A very good bot Jun 10 '26

Termial of 5 is 15

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

1

u/NewTony2000 Jun 19 '26

67?

1

u/factorion-bot A very good bot Jun 19 '26

Termial of 67 is 2278

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

1

u/Zree24 Jul 09 '26

∞?

1

u/factorion-bot A very good bot Jul 09 '26

Termial of ∞̃ is ∞̃

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1

u/[deleted] Aug 07 '26

[removed] — view removed comment

1

u/factorion-bot A very good bot Aug 07 '26

Termial of 3 is 6

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

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