Try:
In symbols
How it was read
Related statements
When a negation flips an inequality (< becomes ≥), it assumes the variables are real numbers.
Try:
In words
How it was read
Related statements
When a negation flips an inequality (< becomes ≥), it assumes the variables are real numbers.
Put the sentence you were given on the left and your symbolic version on the right. The checker compares what they actually mean, so a correct answer written a different way still counts.
Practice pairs:
The sentence in symbols
Your symbols read back in words
Symbol guide and phrases the translator understands
| Symbol | Read it as | Type it as |
|---|---|---|
| ∀ | for all, for every | forall |
| ∃, ∃! | there exists, there exists a unique | exists |
| ¬ | not, it is not the case that | ~ or not then a space |
| ∧ | and | /\ or and |
| ∨ | or (inclusive: one or both) | \/ or or |
| ⇒ | implies; if … then … | => |
| ⇔ | if and only if (iff); is equivalent to | <=> or iff |
| ∈, ∉ | is an element of, is not an element of | x in R becomes x ∈ ℝ |
| ℕ ℤ ℚ ℝ ℂ | natural numbers, integers, rationals, reals, complex numbers | N Z Q R C after ∈ |
| ∣, ∤ | divides, does not divide (2 ∣ n means n is even) | | (a single bar) |
| ≤ ≥ ≠ | at most, at least, not equal to | <= >= != |
| x² | x squared | x^2 |
Phrases you can use in words
- for all / for every / for any … , …
- there exists / there is / for some … such that …
- there exists a unique / exactly one …
- if … then … ; … if … ; whenever
- … only if … ; … implies …
- … if and only if … ; … iff …
- … unless … ; … is necessary / sufficient for …
- it is not the case that … ; not …
- … and … ; either … or … ; both … and …
- is even / odd ; divides ; is divisible by ; is a multiple of
- is an integer / a real number / rational / irrational
- is positive / negative / non-negative / zero
- is greater than / less than / at least / at most
- is equal to / equals / is not equal to ; is between … and …
- squared, cubed, the square root of, plus, minus, times
- Words with no standard symbol (like “is prime”) stay in words.