Real Analysis I · Proof Foundations
Injective compositions
Problem
If $f:X\to Y$ and $g:Y\to Z$ are injective, prove $g\circ f$ injective. Prove injectivity of the composite forces $f$ injective but not necessarily $g$.
Hint
Peel off $g$ and then $f$ from equal composite values.
Check your work
Work the problem yourself first. Then open it in Training to check your answer and read the full worked solution.
Create a free account to check your answer and see the solution. Create a free account.
More Real Analysis I practice problems
- Negating alternating quantifiersProof Foundations
- Integer part of a real numberFoundations & Completeness
- Shrinking nested intervalsFoundations & Completeness
- Why closedness alone is insufficientTopology & Compactness
- Compact sets have finite epsilon-netsTopology & Compactness
- Comparison using bounded partial sumsSequences & Series
- Summable increments force sequence convergenceSequences & Series
- Uniform limits preserve a common Lipschitz boundContinuity
- Connected preimages need not be connectedContinuity