Metrics API: Rename Cumulative to Counter (open-telemetry#47)

* Rename Cumulative to Counter

* Reword that

* More explanation and caveats

* More explanation and caveats

oteps/0000-cumulative-to-counter.md

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+# Rename "Cumulative" to "Counter" in the metrics API
+
+**Status:** `proposed`
+
+Prefer the name "Counter" as opposed to "Cumulative".
+
+## Motivation
+
+Informally speaking, it seems that OpenTelemetry community members would prefer to call Cumulative metric instruments "Counters".  During conversation (e.g., in the 8/21 working session), this has become clear.
+
+Counter is a noun, like the other kinds Gauge and Measure.  Cumulative is an adjective, so while "Cumulative instrument" makes sense, it describes a "Counter".
+
+## Explanation
+
+This will eliminate the cognitive cost of mapping "cumulative" to "counter" when speaking about these APIs.
+
+This is the term used for a cumulative metric instrument, for example, in [Statsd](https://github.com/statsd/statsd/blob/master/docs/metric_types.md) and [Prometheus](https://prometheus.io/docs/concepts/metric_types/#counter).  
+
+However, we have identified important sub-cases of Counter that are treated as follows.  Counters have an option:
+
+- True-cumulative Counter: By default, `Add()` arguments must be >= 0.
+- Bi-directional Counter: As an option, `Add()` arguments must be +/-0.
+
+Gauges are sometimes used to monitoring non-descending quantities (e.g., cpu usage), as an option:
+
+- Bi-directional Gauge: By default, `Set()` arguments may by +/- 0.
+- Uni-directional Gauge: As an option, `Set()` arguments must change by >= 0.
+
+Uni-directional Gauge instruments are typically used in metric `Observer` callbacks where the observed value is cumulative.
+
+## Trade-offs and mitigations
+
+Other ways to describe the distinction between true-cumulative and bi-directional Counters are:
+
+- Additive (vs. Cumulative)
+- GaugeDelta (vs. Gauge)
+
+It is possible that reducing all of these cases into the broad term "Counter" creates more confusion than it addresses.
+
+## Internal details
+
+Simply replace every "Cumulative" with "Counter", then edit for grammar. 
+
+## Prior art and alternatives
+
+In a survey of existing metrics libraries, Counter is far more common.