reactiveValues; for values to be 'floating', and not `fixed`.

reactiveValue.R

ui <- fluidPage(
  actionButton("minus", "-1"),
  actionButton("plus", "+1"),
  br(),
  textOutput("value")
)

# The comments below show the equivalent logic using reactiveValues()
server <- function(input, output, session) {
  value <- reactiveVal(0)       # rv <- reactiveValues(value = 0)

  observeEvent(input$minus, {
    newValue <- value() - 1     # newValue <- rv$value - 1
    value(newValue)             # rv$value <- newValue
  })

  observeEvent(input$plus, {
    newValue <- value() + 1     # newValue <- rv$value + 1
    value(newValue)             # rv$value <- newValue
  })

  output$value <- renderText({
    value()                     # rv$value
  })
}

shinyApp(ui, server)