Chemically, if we were playing “which one is not like the others” with artificial sweeteners, we’d choose Aspartame. Unlike most of the artificial sweeteners, it’s not a carbohydrate.

It’s not “zero calorie” in the way that many artificial sweeteners are, but is still used because it’s considerably sweeter than glucose, and can be used to greatly reduce the calorie content of a food. It’s quite common in diet sodas, but not typically found in anything that is heated as part of the food preparation process, as the molecule does not survive intact.
Aspartame was discovered in 1965 because James Schlatter licked it off of his finger. It does not taste precisely the same as sugar. Although it is sweet, it takes somewhat longer for taste buds to register it as sweet and it has an aftertaste. It’s frequently mixed with other artificial sweeteners.
It’s been approved and disapproved for human consumption on several occasions- it’s currently approved by the FDA and considered well studied. The general idea seems to have been that aspartame is relatively safe, unless you have a reason to be avoiding phenylalanine.
The current (not quite two weeks ago!), relevant question on Aspartame is: Does it cause cancer? There’s some new research out, suggesting that it does, though the FDA disagrees. The implication is that there may be a link between aspartame consumption and liver cancer, though the conclusion seems to be “further study needed”.
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