Mathematics Project.

1. root means the nonnegative number whose square is .
3. product u × v means the cross product of vectors u and v
4. Numbers ℝ means the set of real numbers.
6. subgroup H < G means H is a proper subgroup of G.
7. x ⊥ y means x is perpendicular to y; or more generally x is orthogonal to y.
9. A ≤ B means the problem A can be reduced to the problem B. Subscripts can be added to the ≤ to indicate what kind of reduction.
11. Sometimes used in proofs before reasoning.
12. a * b means the product of a and b.
14. sign −3 means the negative of the number 3.
18. x ≠ y means that x and y do not represent the same thing or value.

1. 9 − 4 means the subtraction of 4 from 9.
2. 6 ± 3 means both 6 + 3 and 6 − 3.
5. Sometimes used in proofs before logical consequences.
6. y ∝ x means that y = kx for some constant k.
8. product u · v means the dot product of vectors u and v
10. ∞ is an element of the extended number line that is greater than all real numbers; it often occurs in limits.
13. x || y means x is parallel to y.
15. ℤ means {..., −3, −2, −1, 0, 1, 2, 3, ...}.
16. x = y means x and y represent the same thing or value.
17. 6 ÷ 3 or 6 ⁄ 3 means the division of 6 by 3.