Limit
A limit is the value a function or sequence approaches as its input approaches a specified point.
At a glance
Key signals
0% cross fields · reaches 1 more
- Mathematical Analysis
- Explanation
- Examples
- Misconception
- Sourced relations
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
Enables · leads to
Continuitydepends onLimitEstablished
Continuity depends on Limit.
Mechanism: A function is continuous at a point when its limit there equals its value.
Derivativedepends onLimitEstablished
Derivative depends on Limit.
Mechanism: The derivative is defined as the limit of a difference quotient.
Riemann integraldepends onLimitEstablished
Riemann integral depends on Limit.
System context
Limitis part ofReal analysisEstablished
Limit is a part of Real analysis.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Currently dark in the atlas: no key date stored · 5 of 5 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Structural neighbourhood: 5 → 14 → 27 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
All 5 of its relationships stay within its own discipline — a field-specific concept in the current atlas.
structural · Structural graph analysis — not a claim of importance, causation or history.
cross-field
5 within-field, 0 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
- No dated history stored — the atlas records no key date for this concept. atlas representation
Conditions
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Dependency radial
What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.
What builds on this
3 concepts build on this directly, 6 in total, across 3 disciplines.
Structural downstream reach along dependency edges — not a claim of historical necessity.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Derivative, Continuity, Convergence of a sequence and Real analysis.
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
This idea also appears in…
The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”
Concepts
explicitly analogous
- Connects 5 other ideas across 1 discipline.
- Most of its connections are of the “Dependency” kind.
Derived from the graph’s real structure — observations, not a score.
Sources
- Derivative without limit (1986) verified
- Direct Iterative Algorithm for Limit Lower Limit Analysis of Axisymmetric Structures (2024) verified