A bear market is a period of sustained decline in the prices of an index or a market, conventionally described as beginning once prices have fallen roughly 20 percent from a recent high and continuing until they have recovered. The threshold is not something the page has invented or that only commentators use: the Securities and Exchange Commission's own investor glossary describes a bear market as a time when stock prices are declining and sentiment is pessimistic, occurring "generally" when a broad market index falls by 20 percent or more over at least a two-month period. That is investor education rather than a rule. The phrase appears nowhere in the Code of Federal Regulations, nothing turns on it legally, and no body publishes dates for the episodes it names.
The convention deserves a careful correction rather than a debunking. It is genuinely useful, in the same way that "a hard frost" is useful, because it separates the ordinary noise of markets from the episodes people remember. It is simply not a measurement anyone is obliged to make in a particular way, and four choices sit inside every use of it: which index is being measured, which prior high counts as the peak, whether the prices are closing prices or intraday highs and lows, and how long the decline must persist to count. The SEC's description answers the last of those with two months and leaves the rest open, and plenty of accounts that quote the 20 percent figure drop the duration condition entirely. Two commentators using different answers can date the same episode differently, or disagree about whether it qualified at all.