What is the meaning of ∃?

math symbols

27,341

Solution 1

It is called a quantifier. It means "there exists".

When used in an expression such as

∃x s.t. x > 0

It means "There exists a number x such that x is greater than 0."

Its counterpart is ∀, which means "for all". It's used like this:

∀x, x > 0

Which means "For any number x, it is greater than 0."

Solution 2

It is the "existential quantifier" as opposed to the upside-down A (∀) which means "universal quantifier." It should be read as "there exists" or "for some". It is a predication that means that some relation or property holds true for at least one object in the domain.

Examples:

An integer n is composite if ∃ integer m such that m > 1 and m < n with n divisible by m.

An integer n is prime if ∀ integer m such that m > 1 and m < n it is true that n is not divisible by m.

A function f is continuous on a metric space (X, d) if ∀x∀ε>0∃δ>0 | ∀y d(x, y) < δ => d(f(x), f(y)) < ε

Solution 3

It is called existential quantifier and being followed by x, it means there exists at least one x

Solution 4

More Info on Predicate Logic

Solution 5

For future reference, wikipedia has a table of mathematical symbols, with an explanation of the meaning(s) of each one.

View more solutions

27,341

Yada

Software Developer living and working in Toronto, Canada. https://fantasysupercontest.com

Updated on July 09, 2022

Comments

Yada almost 2 years

Reading a book on algorithms. Can someone explain the meaning of the mathematical symbol ∃?
- Raymond Tran over 14 years
  
  Discrete structures during the winter session? Ouch.
- Jon Seigel over 14 years
  
  Belongs on MathOverflow mathoverflow.net
- Randolpho over 14 years
  
  Set theory and predicate logic are 100% programming related, whomever voted to close. Although MathOverflow.net is better for pure math questions, obviously.
- Pod over 14 years
  
  Given that this kind of predicated logic is a staple of CS courses, I don't see why it should be closed.
- Jon Seigel over 14 years
  
  @Randolpho: Definitely. However, that has no connection to the question that was asked.
- sdcvvc over 14 years
  
  MO is not a math equivalent of SO. This question would be closed there. ("intended audience is professional mathematicians, mathematics graduate students, and advanced undergraduates." from FAQ)
- Jason S over 14 years
  
  I'm voting to reopen. A similar question was asked recently about ∀ (see stackoverflow.com/questions/1925979/…). Also it definitely does NOT belong on MathOverflow -- that's for Serious mathematical research questions; a question like this would get shut down before you could say ∀ B Ↄ....
- Chris McCauley over 14 years
  
  Agreed this should be allowed. Developers should know how to write invariants, pre-conditions and post-conditions. Perfectly reasonable for someone learning the trade to ask this question.
- Jon Seigel over 14 years
  
  meta.stackexchange.com/questions/9658/…
- ire_and_curses over 14 years
  
  @Jon Seigel: The top answer, from your link - "I would say Math questions are suitable as long as they tie into a programming concept." The explanation is required to understand an algorithm text. Voting to reopen.
- Jon Seigel over 14 years
  
  @ire_and_curses: The question here does not reference any algorithm or programming concept, therefore it is a math question.
- Brian Campbell over 14 years
  
  Someone who does not understand what ∃ means might not know that this is a math question. Should questions on O notation be closed because they are math questions? While it's a mathematical notation, it's usually used in analysis of algorithms. How is someone reading an algorithms text supposed to know that ∃ is any different?
- Jon Seigel over 14 years
  
  Questions on O notation are always linked to algorithms, or a specific example of an algorithm. What is the context in this question? Fair point about not knowing this is a math question. However, it makes me wonder why the book the OP is reading does not contain a definition for the terminology? Any textbook I've read has a dictionary of symbols somewhere in it.
- jason over 14 years
  
  @Jon Seigel: The book almost surely does, the OP just overlooked it. Even the most advanced textbooks often have a table of symbols page somewhere just because there are inconsistencies between authors.
- silbana over 14 years
  
  This is simply inane. Are we going to have a question for every mathematical symbol on Earth? Let me get it going: What is <b>א<sub>0</sub></b>?
- Eric Wilson almost 13 years
  
  This belongs on math.stackexchange.com, which didn't exist during all of the previous discussion.
- Eric Wilson over 12 years
  
  Three months later, I'm curious why this has not been migrated to Math.SE.
Kieveli over 14 years

I thought that was the other way around... Huh. Learn something new every day: en.wikipedia.org/wiki/%E2%88%83
sdcvvc over 14 years

Quantifier. Predicates are something different: en.wikipedia.org/wiki/Predicate_(mathematical_logic)
Welbog over 14 years

@sdcvvc: Righto! Been a few years since my mathematical logic course. :) I've corrected the answer.
Randolpho over 14 years

@Kieveli: Backwards "E" for "Exists", upside-down "A" for "All". That should help you, mnemonically.
Niklas Rosencrantz over 14 years

Yes and ∀ you can implement complementary to ∃ since ∀x means there is no x not...eg ∀x and ∄x~ are same
Andrew over 14 years

We used a syntax ∀x(x>0) and ∃x(x > 0)
Welbog over 14 years

Oh no not the epsilons and deltas! Calculus 1 is flooding back to me now. I have only you to blame, Jason.
Welbog over 14 years

Ah, whom am I kidding? I loved Calculus 1. That's why I took Calculus 2 and Calculus 3! Thanks for that trip down memory lane.
starblue over 14 years

@Randolpho Both letters are rotated by 180 degrees, they just happen to have different symmetries.
starblue over 14 years

Alternating between quantifiers produces formulas which are both hard to understand and hard to handle algorithmically. For example, the definition of continuity has the pattern ∀∃∀ (the ∀x∀y is missing in the example).