1:1

Do you mean one of these?

• Ratios/proportions (1:1 means equal quantities)
• A 1:1 mapping in discrete math (one-to-one correspondence, i.e., injective/bijection)
• something else (e.g., a 1:1 appointment, scaling, etc.)

If you’re preparing for exams, here are quick notes and tiny problems for the two most common interpretations:

1. Ratios and proportions (1:1 means equal)

• Meaning: two quantities are equal in amount.
• Key facts:
  • a:b = 1:1 implies a = b.
  • If a:b = 1:1 and a + b = T, then a = b = T/2.
• Quick examples:
  • If a:b = 1:1 and a + b = 40, then a = b = 20.
  • In a recipe with flour:sugar = 1:1 and total flour + sugar = 500 g, each is 250 g.
• Practice problems:
  • Problem: A mixture has ratio 1:1 of chemical A to chemical B and total mass is 300 g. How much of each chemical? Answer: 150 g of A and 150 g of B.
  • Problem: You need a solution with 1:1 ratio of solute to solvent and you want 1 L total. How much solute and solvent? Answer: 0.5 L solute and 0.5 L solvent.

2. One-to-one mapping (1:1) in functions/discrete math

• Meaning: a function is 1:1 (injective) if different inputs map to different outputs. If also onto, it’s a bijection (one-to-one correspondence).
• Quick rules:
  • Injective: f(x1) = f(x2) implies x1 = x2.
  • Bijective: every element of the target has a preimage.
• Simple example:
  • f: {1,2,3} -> {a,b,c} with f(1)=a, f(2)=b, f(3)=c is 1:1 (and onto) – bijection.
  • g: {1,2,3} -> {a,b} with g(1)=a, g(2)=a, g(3)=b is not 1:1 (not injective).
• Quick exercise:
  • Determine if a given mapping is 1:1: If f(1)=5, f(2)=5, is it injective? No, because two inputs map to the same output.
  • If domain and codomain have the same finite size and the mapping is injective, it’s also bijective.

What would you like to focus on? A quick set of practice problems in your preferred interpretation, or a deeper explanation with more examples? If you can share the course or topic (e.g., algebra, calculus, discrete math), I’ll tailor it to that exam.