Alphabeta Math

The Exponential Function: Examples and Counterexamples

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✓ 7 results · all verified · 2 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 5 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
Abstract Algebra
Combinatorics
Linear Algebra
Real Analysis
Set Theory
Topology
2 · Logical flowchart

3 · Items

Example

The log-free product limit (1-2/n)ⁿ→exp(-2)

Counterexample

The convergence (1+x/n)ⁿ→exp x is not uniform on ℝ

Example

The one-sided flat function is C^∞ with identically zero Taylor series

Counterexample

A smooth function not equal to its Maclaurin series

Example

A nonzero smooth compactly supported bump

Counterexample

A discontinuous positive solution of F(x+y)=F(x)F(y)

Counterexample

The exponential is not uniformly continuous on ℝ

Sources