Is there a symbol for "probably equals"?

  • B
  • Thread starter John Bartle
  • Start date
  • Tags
    Symbol
In summary, there are various symbols that can be used to express the concept of "probably equals" depending on the context and the degree of quantification, such as ≈, ~, ≡, =, ?, P( ), ±, =_a.e., ∈, ⊆, ≜, ≃, ≐, and ≅. However, there is no specific symbol for "I have no idea but I guess probably..." and it would ultimately depend on the author's interpretation. Additionally, the concept of "necessarily equals" can also be expressed using symbols such as =_a.c. or ===, but it is important to note that this may not always be equivalent to regular equality.
  • #1
John Bartle
20
1
Is there a symbol for "probably equals" ?

An example would be A probably equals B.
 
Mathematics news on Phys.org
  • #2
There’s one for approximately equals ie an equals with a wave mark over it and one for identically equals I think it’s an equals with a third horizontal Lin and one for not sure if they’re equal ie an equals sign with a question mark over it.

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

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

Here’s a discussion on Math Stack Exchange but it seems sadly there is not:

https://math.stackexchange.com/questions/1446010/symbol-for-probably-equal-to-barring-pathology
 
Last edited:
  • #3
@jedishrfu

Thanks. I'd rather have a probably equals symbol but I think I might just settle for the ≟ or the a.s. notation.
 
  • #4
John Bartle said:
Is there a symbol for "probably equals" ?

An example would be A probably equals B.
Depends on what probably means! If you do not know, then the question mark makes sense: ##\stackrel{?}{=}##. If it is equal up to finitely many exceptions, or if the exceptions are otherwise a set of measure zero, then you can write ##{=}_{a.e.}## for "almost everywhere". Thus it all depends on what is "probably" to you. If you actually have a probability, then it is ##P(x=a) = c\% ## with possibly an error margin ##\pm e\%## behind it.
 
Last edited:
  • Like
Likes berkeman, Klystron and mfb
  • #5
John Bartle said:
@jedishrfu

Thanks. I'd rather have a probably equals symbol but I think I might just settle for the ≟ or the a.s. notation.
I don't read that
##X## "probably equals ##Y## as meaning X equals Y in probability ##X =_p Y##. Also saying ##X =_{a.s} Y## i.e. that X equal Y almost surely is a stronger criterion that X equals Y in probability.

This is tagged as B thread. If that tagging is correct, please don't use almost surely for anything as you'll misuse it
-- I'm pretty (almost?) sure on this.
 
  • Like
Likes jedishrfu
  • #6
@StoneTemplePython

I'm not real good with math in general, and I know even less concerning probability and statistics. What notation, for example, would you think makes sense for the statement:

cat very likely equals animal

I know cat is a subset of animal, but most people say a cat IS an animal also. I also want to point out the fact that it is only very likely an animal because nothing/not much is certain.I would just go with cat =a.s. animal
 
  • #7
John Bartle said:
@StoneTemplePython

I'm not real good with math in general, and I know even less concerning probability and statistics. What notation, for example, would you think makes sense for the statement:

cat very likely equals animal

I know cat is a subset of animal, but most people say a cat IS an animal also. I also want to point out the fact that it is only very likely an animal because nothing/not much is certain.I would just go with cat =a.s. animal

I appreciate the question but there are 2 big issues. One is that equalities run both ways so you need to be careful... I don't think people would claim an animal is a cat. You have the right idea with subsets. Why not ##\text{cat} \subset \text{animal}## with an asterisk saying that you are highly confident of this? Almost surely is a much stronger claim than this and I don't think that is what you are trying to say.

The other issue which really is a dead-end in philosophy (which is outside the scope of these forums) is a lot of people may define a cat to be a kind of animal -- once you start arguing about definitions and 'true meaning' it doesn't really go anywhere, and I don't think math (including probability) has much to say here.
 
  • #8
StoneTemplePython said:
One is that equalities run both ways so you need to be careful... I don't think people would claim an animal is a cat.

Oh yeah, I forgot about that.

StoneTemplePython said:
You have the right idea with subsets. Why not ##\text{cat} \subset \text{animal}## with an asterisk saying that you are highly confident of this?

Uhh. Yeah, I might use the subset and an asterisk symbol. I'm not sure if that fits with my particular situation, but I'll consider it.Thanks for your help.
 
  • #10
If probably means likely in its linguistic sense, then it is not a mathematical expression and thus there is no sign for it. If it is quantifiable in any sense, then there are signs which depend on the context and the degree of quantification.
 
  • #12
Depending on context:

##\approx\quad \sim \quad\equiv\quad =\quad \stackrel{?}{=} \quad P(\ldots) \quad \pm \quad=_{a.e.}\quad \in \quad \subseteq \quad \triangleq\quad\circeq \quad \doteq \quad \cong \quad \fallingdotseq ##

There is no sign for: "I have no idea but I guess probably ..."
 
  • Like
Likes dextercioby and Janosh89
  • #13
Ahh okay. I didn’t think of those in a probalistic sense.
 
  • #14
If they are not otherwise used, authors will have some freedom to attach a certain meaning as all signs are context sensitive. In any case, there has to be a definition, although I would avoid regular signs as ##=## or ##\cong## etc. It always comes back to what probably means. I think I would write is as ##=_{a.c.}## for "almost certain".
 
  • #15
jedishrfu said:
A better one might be a % over the equals
I can't find that symbol. Can you tell me where I would find it?
 
  • #16
Hey does anyone know if there is a symbol for "A necessarily equals B" ?


An example would be "ball necessarily equals sphere" or maybe "truth necessarily equals (not falsity)"
 
  • #17
Two different things here.
John Bartle said:
An example would be "ball necessarily equals sphere"
A ball is a subset of a sphere. They are not equivalent.

John Bartle said:
or maybe "truth necessarily equals (not falsity)"

This one is kind of a truism***.

To a programmer, it might be pedantically expressed as
T == !F or T==!T

== means exactly the same as
!
means logical NOT
!
means logical NOT NOT

So, T is exactly the same as NOT F
Or T is exactly the same as NOT NOT T.

Finally,
T === !F
means T is the very same thing as !F.
But that might be overstating the case.***This assumes truth and falsehood are binary and there are no middle values. Not a good assumption.
Some things are not true, yet also not false. Saying "I bought five eggs" when in fact I bought six is not false, but it's also not the truth. It is a partial truth.
 
Last edited:
  • Like
Likes Klystron and jedishrfu
  • #18
A sphere is a subset of a (sufficiently large) ball or a boundary of a closed ball.

For modal logic we use the symbol ##\diamond ## to mean "possibly". So if we have a statement ##P ## asserting the equality of something, writing ##\diamond P ## would mean the equality is possibly valid.

I am grossly over-simplifying, though.

I don't think there is any special notation for something as vague as "probably equals". We could write ## \mathbb P (P) = 0.7## or something tangible like that.
 
Last edited:
  • #19
John Bartle said:
Is there a symbol for "probably equals" ?
A variable.
John Bartle said:
An example would be A probably equals B.
If A and B are not variables then A doesn't equal B. You can't compare two values without reading them, that is guessing and trying to compare. Your "probably" is selecting the right data type in software dev terms.
 
  • #20
In some non-binary logic where the "truthlikeness" of a statement is a real number between 0 and 1, you could say that "truthlikeness of a=b is greater than 0.9" or similar.
 
  • #21
@John Bartle you have been pursuing this notion for several posts. However it appears that there is no such symbol. Perhaps because one can’t use for anything other than what you want a shorthand for probably equals.

We have three categories already:
- things equal
- things we don’t know are equal
- things not equal

To which you want to add:
- things probably equal
- things probably not equal

To the list where maybe quantum computing would benefit but I have yet to see that and so offered the % over equals in the interim.

It’s an invention based on past equals symbolic conventions and I have no reference for it. I leave to future posters to come up with a probably not equals symbol.
 
Last edited:
  • #22
We can all agree what it means for two expressions to be equal. Or not. But I don't think we can agree on what it even means to be "probably" equal. 95% chance of being equal? A 90% chance of being within 5%? And if we can't agree on what we are talking about, why do we need a symbol for it?
 
  • Like
Likes dextercioby and dRic2
  • #23
jedishrfu said:
@John Bartle you have been pursuing this notion for several posts. However it appears that there is no such symbol.

Yeah, I noticed. But in post #16 "I asked Hey does anyone know if there is a symbol for "A necessarily equals B"" It seems like this new question is relevant enough to my original post and needs that it would be on topic to ask. I don't see why this would be against the rules. I figure if no one wants to further engage then I'll stop posting. I guess that's acceptable forum etiquette?


I just test the waters to see what general options are available. I do the same thing with words when I look for synonyms. Even though most synonyms would practically work I still will look for that "special" synonym.
 
Last edited:
  • #24
It wasn’t against the rules, I was worried that you were pursuing something that just doesn’t exist yet and maybe never will. We alll get stuck in this notion of there has to be something and if I search long enough I’ll find it.
 
  • #25
jedishrfu said:
It wasn’t against the rules, I was worried that you were pursuing something that just doesn’t exist yet and maybe never will. We alll get stuck in this notion of there has to be something and if I search long enough I’ll find it.

Lol, so true...:smile:
 
  • Like
Likes jedishrfu
  • #26
v_A = cat
v_A = v_B when v_B = cat or animal or feline or etc...
v_A = v_B if v_B = cat, animal, feline, etc...
v_A = v_B where v_B like cat or animal or feline or etc...
if v_B = cat, animal, feline, etc... then v_A = v_B
when v_B = cat or animal or feline or etc... then v_A = v_B
where v_B like cat or animal or feline or etc... then v_A = v_B

probability added before or after the compare with the if, where and when clauses.
 
  • #27
John Bartle said:
Is there a symbol for "probably equals" ?

An example would be A probably equals B.

I was actually talking about this with a friend yesterday.

We were discussing about 0^0 and how it "probably" be 1. Even the maths implies that it would eventually be 1, but without an infinite number of equations it fails.
For instance 0^google would still be 0, because Google is still a countable number.
But when doing 0^0 , the closer you get to powering 0 by 0, the closer your answer comes to 1.

So if you do find a symbol tell me so I can apply it to 0^0 (probably)= 1
EZ1gFzJ.jpg
 

Attachments

  • EZ1gFzJ.jpg
    EZ1gFzJ.jpg
    27.2 KB · Views: 778
  • #28
slappmunkey said:
I was actually talking about this with a friend yesterday.

We were discussing about 0^0 and how it "probably" be 1. Even the maths implies that it would eventually be 1, but without an infinite number of equations it fails.
For instance 0^google would still be 0, because Google is still a countable number.
But when doing 0^0 , the closer you get to powering 0 by 0, the closer your answer comes to 1.

So if you do find a symbol tell me so I can apply it to 0^0 (probably)= 1
View attachment 238513

Do you mean "googol"?

https://en.wikipedia.org/wiki/Googol
 
  • Like
Likes jedishrfu
  • #29
PeroK said:
Do you mean "googol"?

https://en.wikipedia.org/wiki/Googol
I like how you phrase that in a question like it isn't obvious... I'm not trying to be rude but you clearly see it's a typo, you clearly know what I'm talking about... So is it really that worth it to nit pick an error that was autocorrect anyways?

It would have been better to just simply state that I made a typo, not ask me like I'm too stupid too see... Kind of insulting. I'm a grown man, if I make a typing error (on my phone God forbid) just tell me, you don't have to be cynical about it.
 
  • #30
slappmunkey said:
I like how you phrase that in a question like it isn't obvious... I'm not trying to be rude but you clearly see it's a typo, you clearly know what I'm talking about... So is it really that worth it to nit pick an error that was autocorrect anyways?

It would have been better to just simply state that I made a typo, not ask me like I'm too stupid too see... Kind of insulting. I'm a grown man, if I make a typing error (on my phone God forbid) just tell me, you don't have to be cynical about it.

A lot of people, for the obvious reason, think that the number is spelled the same as the engine. I thought it was worth pointing it out.
 
  • #31
No need to be overly sensitive here. All of us have experienced the case of using the wrong word from time to thyme and the spell checker misses or mangles it.

Recently my phone corrector had done that just as i sent a text, changing a misspelled word to a womans name in a text to my wife.
 
Last edited:
  • Like
Likes Klystron
  • #32
PeroK said:
A lot of people, for the obvious reason, think that the number is spelled the same as the engine. I thought it was worth pointing it out.
I pwned guy once who was certain it was spelled Google. He'd never known they were two different words.
 
  • #33
slappmunkey said:
I like how you phrase that in a question like it isn't obvious... I'm not trying to be rude but you clearly see it's a typo, you clearly know what I'm talking about... So is it really that worth it to nit pick an error that was autocorrect anyways?

It would have been better to just simply state that I made a typo, not ask me like I'm too stupid too see... Kind of insulting. I'm a grown man, if I make a typing error (on my phone God forbid) just tell me, you don't have to be cynical about it.

The problem with the internet is we forget that we just don't know peoples ages, gender, accents, languages... and consequently don't know what to take as a basis for conversation.
 

1. What does "probably equals" mean in scientific notation?

In scientific notation, "probably equals" is a symbol used to indicate that two values are likely to be equal, but there is a small chance that they may not be exactly equal.

2. Is there a specific symbol for "probably equals"?

Yes, the symbol for "probably equals" is a combination of the equal sign (=) and the tilde (~) symbol, written as "≈".

3. How is "probably equals" different from "equals" in scientific notation?

"Equals" in scientific notation indicates that two values are exactly equal, while "probably equals" indicates that there is a small chance they may not be exactly equal.

4. Can "probably equals" be used in all scientific fields?

Yes, "probably equals" can be used in all scientific fields as it is a universally recognized symbol in scientific notation.

5. Are there any other symbols that have a similar meaning to "probably equals"?

Yes, there are other symbols that can be used to indicate a similar meaning to "probably equals", such as "≅" (approximately equal) and "≃" (approximately equivalent).

Similar threads

Replies
6
Views
801
Replies
35
Views
2K
Replies
9
Views
1K
  • General Math
Replies
12
Views
1K
Replies
12
Views
4K
Replies
3
Views
914
Replies
12
Views
918
  • General Math
Replies
2
Views
1K
  • General Math
Replies
3
Views
1K
Replies
2
Views
1K
Back
Top