What are these symbols? - Numberphile

Asaf Karagila discusses some of the symbols used in Logic and Set Theory. More links & stuff in full description below ↓↓↓

* A set theorist's clarification from Asaf commenting on Brady's simplified animations... "By {Primes} we mean the set {2,3,5,7,11,13,...} of prime numbers, rather than the set whose element is the set of prime numbers"

NUMBERPHILE

Videos by Brady Haran

[ZevEisenberg]

Finally someone is explaining all Sixty of these Symbols

[papafreddy]

For anyone who wants to pursue a math major, this will become one of the most helpful videos you'll ever watch, because you'll never stop seeing these symbols no matter which field of math you're in.

[IceMetalPunk]

Learning these symbols in university is one of the most useful things I've ever learned. You can write out, read, and analyze so many logical and mathematical questions in very concise space, and once you're used to it, it's almost like your brain analyzes the statements more efficiently, too. No more having to read a bunch of English words between every important part of a statement: every individual symbol already communicates an entire idea, and they're all the important parts.

[BruceGrembowski]

Talking about aleph reminded me of this song:

Aleph null bottles of beer on the wall,
Aleph null bottles of beer;
Take one down, pass it around:
Aleph null bottles of beer on the wall.

[venisontron]

Three logicians walk into a bar. The bartender asks, "Will you all be having a drink?"
The first logician says, "I don't know."
The second logician says, "I don't know."
The third logician says, "Yes."

[Satokaさとか]

18:56 For anyone wondering why integer is Z, it's from German “Zahlen” which means “numbers”.

[TH_]

This will become one of the most viewed numberphile videos

[ahreuwu]

I can finally understand the last 8 years of numberphile videos

[erifetim]

00:28 ∧ And
01:14 ∨ Or
01:55 ⊕ Exclusive or
02:25 ¬ Negation (sometimes ∼)
03:07 → Implication
03:41 ⟷ If and only if
04:30 ⇒, ⇐, ⇔ Statements about statements (meta-statement)
06:00 ∀, ∃ Quantifiers, ”for all”, ”there exists”
07:37 ∄ Not exists
08:06 Sets
09:14 ∅ The empty set
10:47 A \ B Set difference (”the part of A
11:55 A^C Complement (”the part outside”)
13:25 A ∩ B Intersection (”the common part of A and B”) 14:14 A ∪ B Union (”everything that is in A or in B”)
14:38 ⊂, ⊆ Set inclusion, subset
15:50 ⊂, ⊊ Set inclusion, strict subset
16:14 ⊈ Not a subset
16:43 ∈, ∉ Membership, element of
18:07 Blackboard bolt font, i.e., N
18:29 ℕ The set of natural numbers (0 is a natural number)
18:57 ℤ The set of integers
19:18 ℚ The set of rational numbers
19:51 ℝ The set of real numbers
20:09 ℂ The set of complex numbers
20:24 Hebrew letters Aleph, Beth, Gimel Daleth

[shooty]

Loving the subtle addition of -1/12 in *Q*

[BenWard]

I (for one) would love to see more videos on symbology and notation. I think it is one of the things that can be really overwhelming when you are trying to wrap your head around a new mathematical concept. Peeling back the layers of abstraction is what you do best, Brady!

[TheMitchyevans]

The lack of explanation for the symbols has often been my undoing to understanding many Wikipedia articles on mathematics. Thank you for filling that gap.

[Kr-nvfo]

Professor Blackboard Boldface was truly one of the best maths popularisers of his time.

[sandekv]

As a Norwegian, I cinsider the empty set to be a different symbol from Ø. Our letter tends to be taller and aligned like O but with a slash, while the empty set tends to be perfectly round and not aligned to the baseline of your writing. They do look very similar though.

[gtziavelis]

I like Numberphile Λ I look forward to next Numberphile video

[pelegrak]

"what are these symbols?"
-an unsuspecting student joining the calc 2 course

[PeterFreese]

This was a much-needed refresher, and delightful to hear Brady jumping ahead in understanding as Asaf explains.

[insouciantFox]

∃! will always be my favourite one.
There exists exactly one. Not useful in pure math, but for note-taking, it's awesome.

[judahkozel]

This video is amazing. Please do the rest of the symbols because that would be excellent.

[Bostonceltics]

My intro to discreet mathematics professor would really appreciate you explaining this. 😂
They complained about the way we overused and misused the implication arrows. There's just not enough time in most of your academic career to get the background needed. Appreciate the supplement.❤