How do children form beliefs about the infinity of space, time, and number? We asked whether children held similar beliefs about infinity across domains, and whether beliefs in infinity for domains like space and time might be scaffolded upon numerical knowledge (e.g., knowledge successors within the count list). To test these questions, 112 U.S. children (aged 4;0–7;11) completed an interview regarding their beliefs about infinite space, time, and number. We also measured their knowledge of counting, and other factors that might impact performance on linguistic assessments of infinity belief (e.g., working memory, ability to respond to hypothetical questions). We found that beliefs about infinity were very high across all three domains, suggesting that infinity beliefs may arise early in development for space, time, and number. Second, we found that—across all three domains—children were more likely to believe that it is always possible to add a unit than to believe that the domain is endless. Finally, we found that understanding the rules underlying counting predicted children’s belief that it is always possible to add 1 to any number, but did not predict any of the other elements of infinity belief.

We introduce a new resource: the SAYCam corpus. Infants aged 6–32 months wore a head-mounted camera for approximately 2 hr per week, over the course of approximately two-and-a-half years. The result is a large, naturalistic, longitudinal dataset of infant- and child-perspective videos. Over 200,000 words of naturalistic speech have already been transcribed. Similarly, the dataset is searchable using a number of criteria (e.g., age of participant, location, setting, objects present). The resulting dataset will be of broad use to psychologists, linguists, and computer scientists.